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The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

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Handbook of K-Theory

Abstract

We give a survey of the meaning, status and applications of the Baum–Connes Conjecture about the topological K-theory of the reduced group C*-algebra and the Farrell–Jones Conjecture about the algebraic K- and L-theory of the group ring of a (discrete) group G.

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References

  1. H. Abels. Parallelizability of proper actions, global K-slices and maximal compact subgroups. Math. Ann., 212:1–19, 1974/75.

    Google Scholar 

  2. H. Abels. A universal proper G-space. Math. Z., 159(2):143–158, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  3. U. Abresch. Über das Glätten Riemannscher Metriken. Habilitationsschrift, Bonn, 1988.

    Google Scholar 

  4. J. F. Adams. Stable homotopy and generalised homology. University of Chicago Press, Chicago, Ill., 1974. Chicago Lectures in Mathematics.

    MATH  Google Scholar 

  5. C. Anantharaman and J. Renault. Amenable groupoids. In Groupoids in analysis, geometry, and physics (Boulder, CO, 1999), volume 282 of Contemp. Math., pages 35–46. Amer. Math. Soc., Providence, RI, 2001.

    Google Scholar 

  6. C. Anantharaman-Delaroche and J. Renault. Amenable groupoids, volume 36 of Monographies de L’Enseignement Mathématique. Geneva, 2000. With a foreword by Georges Skandalis and Appendix B by E. Germain.

    Google Scholar 

  7. D. R. Anderson, F. X. Connolly, S. C. Ferry, and E. K. Pedersen. Algebraic K-theory with continuous control at infinity. J. Pure Appl. Algebra, 94(1):25–47, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. R. Anderson and W. C. Hsiang. The functors K−i and pseudo-isotopies of polyhedra. Ann. of Math. (2), 105(2):201–223, 1977.

    Article  MathSciNet  Google Scholar 

  9. C. S. Aravinda, F. T. Farrell, and S. K. Roushon. Surgery groups of knot and link complements. Bull. London Math. Soc., 29(4):400–406, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  10. C. S. Aravinda, F. T. Farrell, and S. K. Roushon. Algebraic K-theory of pure braid groups. Asian J. Math., 4(2):337–343, 2000.

    MATH  MathSciNet  Google Scholar 

  11. M. F. Atiyah. Global theory of elliptic operators. In Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969), pages 21–30. Univ. of Tokyo Press, Tokyo, 1970.

    Google Scholar 

  12. M. F. Atiyah. Elliptic operators, discrete groups and von Neumann algebras. Astérisque, 32-33:43–72, 1976.

    MathSciNet  Google Scholar 

  13. A. Bak. Odd dimension surgery groups of odd torsion groups vanish. Topology, 14(4):367–374, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Bak. The computation of surgery groups of finite groups with abelian 2-hyperelementary subgroups. In Algebraic K -theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976), pages 384–409. Lecture Notes in Math., Vol. 551. Springer-Verlag, Berlin, 1976.

    Google Scholar 

  15. M. Banagl and A. Ranicki. Generalized Arf invariants in algebraic L-theory. arXiv: math.AT/0304362, 2003.

    Google Scholar 

  16. A. Bartels. On the domain of the assembly map in algebraic K-theory. Algebr. Geom. Topol.(electronic), 3:1037–1050, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Bartels. Squeezing and higher algebraic K-theory. K -Theory, 28(1):19–37, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  18. A.Bartels,F.T.Farrell,L.E.Jones,andH.Reich.Afoliatedsqueezingtheorem for geometric modules. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory. 2003. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001.

    Google Scholar 

  19. A. Bartels, F. T. Farrell, L. E. Jones, and H. Reich. On the isomorphism conjecture in algebraic K-theory. Topology, 43(1):157–231, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  20. A. Bartels and W. Lück. Isomorphism conjecture for homotopy K-theory and groups acting on trees. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 342, Münster, arXiv:math.KT/0407489, 2004.

    Google Scholar 

  21. A. Bartels and H. Reich. On the Farrell-Jones conjecture for higher algebraic K-theory. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 282, Münster, to appear in JAMS, 2003.

    Google Scholar 

  22. H. Bass. Algebraic K -theory. W. A. Benjamin, Inc., New York-Amsterdam, 1968.

    Google Scholar 

  23. H. Bass. Some problems in “classical” algebraic K-theory. In Algebraic K -theory, II: “Classical” algebraic K -theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pages 3–73. Lecture Notes in Math., Vol. 342. Springer-Verlag, Berlin, 1973.

    Google Scholar 

  24. H. Bass. Euler characteristics and characters of discrete groups. Invent. Math., 35:155–196, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  25. H. Bass, A. Heller, and R. G. Swan. The Whitehead group of a polynomial extension. Inst. Hautes Études Sci. Publ. Math., (22):61–79, 1964.

    Article  MATH  MathSciNet  Google Scholar 

  26. P. Baum and A. Connes. Chern character for discrete groups. In A fête of topology, pages 163–232. Academic Press, Boston, MA, 1988.

    Google Scholar 

  27. P. Baum and A. Connes. Geometric K-theory for Lie groups and foliations. Enseign. Math. (2), 46(1-2):3–42, 2000.

    Google Scholar 

  28. P. Baum, A. Connes, and N. Higson. Classifying space for proper actions and K-theory of group C ∗-algebras. In C ∗ -algebras: 1943–1993 (San Antonio, TX, 1993), pages 240–291. Amer. Math. Soc., Providence, RI, 1994.

    Google Scholar 

  29. P. Baum and R. G. Douglas. K-homology and index theory. In Operator algebras and applications, Part I (Kingston, Ont., 1980), pages 117–173. Amer. Math. Soc., Providence, R.I., 1982.

    Google Scholar 

  30. P. Baum, N. Higson, and R. Plymen. Representation theory of p-adic groups: a view from operator algebras. InThe mathematical legacy of Harish-Chandra (Baltimore, MD, 1998), pages 111–149. Amer. Math. Soc., Providence, RI, 2000.

    Google Scholar 

  31. P. Baum and M. Karoubi. On the Baum-Connes conjecture in the real case. Q. J. Math., 55(3):231–235, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  32. P. Baum, S. Millington, and R. Plymen. Local-global principle for the Baum-Connes conjecture with coefficients. K -Theory, 28(1):1–18, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  33. E. Berkove, F. T. Farrell, D. Juan-Pineda, and K. Pearson. The Farrell-Jones isomorphism conjecture for finite covolume hyperbolic actions and the algebraic K-theory of Bianchi groups. Trans. Amer. Math. Soc., 352(12):5689–5702, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  34. E. Berkove, D. Juan-Pineda, and K. Pearson. The lower algebraic K-theory of Fuchsian groups. Comment. Math. Helv., 76(2):339–352, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  35. A. J. Berrick. An approach to algebraic K -theory. Pitman (Advanced Publishing Program), Boston, Mass., 1982.

    MATH  Google Scholar 

  36. A. J. Berrick, I. Chatterji, and G. Mislin. From acyclic groups to the Bass conjecture for amenable groups. Preprint, to appear in Math. Annalen, 2001.

    Google Scholar 

  37. B. Blackadar. K -theory for operator algebras. Springer-Verlag, New York, 1986.

    MATH  Google Scholar 

  38. M. Bökstedt, W.C. Hsiang, and I.Madsen. The cyclotomic trace and algebraic K-theory of spaces. Invent. Math., 111(3):465–539, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  39. A. Borel. Stable real cohomology of arithmetic groups. Ann. Sci. École Norm. Sup. (4), 7:235–272 (1975), 1974.

    Google Scholar 

  40. A. K. Bousfield and D. M. Kan. Homotopy limits, completions and localizations. Springer-Verlag, Berlin, 1972. Lecture Notes in Mathematics, Vol. 304.

    MATH  Google Scholar 

  41. W. Browder. Surgery on simply-connected manifolds. Springer-Verlag, New York, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65.

    MATH  Google Scholar 

  42. M. Burger and A. Valette. Idempotents in complex group rings: theorems of Zalesskii and Bass revisited. J. Lie Theory, 8(2):219–228, 1998.

    MATH  MathSciNet  Google Scholar 

  43. D. Burghelea and R. Lashof. Stability of concordances and the suspension homomorphism. Ann. of Math. (2), 105(3):449–472, 1977.

    Article  MathSciNet  Google Scholar 

  44. S. Cappell, A. Ranicki, and J. Rosenberg, editors. Surveys on surgery theory. Vol. 1. Princeton University Press, Princeton, NJ, 2000. Papers dedicated to C. T. C. Wall.

    MATH  Google Scholar 

  45. S. Cappell, A. Ranicki, and J. Rosenberg, editors. Surveys on surgery theory. Vol. 2. Princeton University Press, Princeton, NJ, 2001. Papers dedicated to C. T. C. Wall.

    MATH  Google Scholar 

  46. S. E. Cappell. Mayer-Vietoris sequences in hermitian K-theory. In Algebraic K-theory, III: Hermitian K-theory and geometric applications (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pages 478–512. Lecture Notes in Math., Vol. 343. Springer-Verlag, Berlin, 1973.

    Google Scholar 

  47. S. E. Cappell. Splitting obstructions for Hermitian forms and manifolds with Z2 ⊂ π1. Bull. Amer. Math. Soc., 79:909–913, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  48. S. E. Cappell. Manifolds with fundamental group a generalized free product. I. Bull. Amer. Math. Soc., 80:1193–1198, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  49. S. E. Cappell. Unitary nilpotent groups and Hermitian K-theory. I. Bull. Amer. Math. Soc., 80:1117–1122, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  50. S. E. Cappell and J. L. Shaneson. On 4-dimensional s-cobordisms. J. Differential Geom., 22(1):97–115, 1985.

    MATH  MathSciNet  Google Scholar 

  51. M. Cárdenas and E. K. Pedersen. On the Karoubi filtration of a category. K -Theory, 12(2):165–191, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  52. G. Carlsson. Deloopings in algebraic K-theory. In this Handbook.

    Google Scholar 

  53. G. Carlsson. A survey of equivariant stable homotopy theory. Topology, 31(1):1–27, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  54. G. Carlsson. On the algebraic K-theory of infinite product categories. K-theory, 9:305–322, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  55. G. Carlsson and E. K. Pedersen. Controlled algebra and the Novikov conjectures for K- and L-theory. Topology, 34(3):731–758, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  56. G. Carlsson, E. K. Pedersen, and W. Vogell. Continuously controlled algebraic K-theory of spaces and the Novikov conjecture. Math. Ann., 310(1):169–182, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  57. D. W. Carter. Localization in lower algebraic K-theory. Comm. Algebra, 8(7):603–622, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  58. D. W. Carter. Lower K-theory of finite groups. Comm. Algebra, 8(20):1927–1937, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  59. J. Chabert and S. Echterhoff. Permanence properties of the Baum-Connes conjecture. Doc. Math., 6:127–183 (electronic), 2001.

    MATH  MathSciNet  Google Scholar 

  60. J. Chabert, S. Echterhoff, and R. Nest. The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 251, 2003.

    Google Scholar 

  61. S. Chang. On conjectures of Mathai and Borel. Geom. Dedicata, 106:161–167, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  62. S. Chang and S. Weinberger. On invariants of Hirzebruch and Cheeger-Gromov. Geom. Topol., 7:311–319 (electronic), 2003.

    Article  MATH  MathSciNet  Google Scholar 

  63. I. Chatterji and K. Ruane. Some geometric groups with rapid decay. preprint, arXiv:math.GT/0310356, 2004.

    Google Scholar 

  64. J. Cheeger and M. Gromov. Bounds on the von Neumann dimension of L2 -cohomology and the Gauss-Bonnet theorem for open manifolds. J. Differential Geom., 21(1):1–34, 1985.

    MATH  MathSciNet  Google Scholar 

  65. J. Cheeger and M. Gromov. On the characteristic numbers of complete manifolds of bounded curvature and finite volume. In Differential geometry and complex analysis, pages 115–154. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  66. P.-A. Cherix, M. Cowling, P. Jolissaint, P. Julg, and A. Valette. Groups with the Haagerup property, volume 197 of Progress in Mathematics. Birkhäuser Verlag, Basel, 2001.

    MATH  Google Scholar 

  67. G. Cliff and A. Weiss. Moody’s induction theorem. Illinois J. Math., 32(3):489–500, 1988.

    MATH  MathSciNet  Google Scholar 

  68. T. D. Cochran. Noncommutative knot theory. Algebr. Geom. Topol., 4:347–398, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  69. T. D. Cochran, K. E. Orr, and P. Teichner. Knot concordance, Whitney towers and L2 -signatures. Ann. of Math. (2), 157(2):433–519, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  70. M. M. Cohen. A course in simple-homotopy theory. Springer-Verlag, New York, 1973. Graduate Texts in Mathematics, Vol. 10.

    MATH  Google Scholar 

  71. A. Connes. Noncommutative geometry. Academic Press Inc., San Diego, CA, 1994.

    MATH  Google Scholar 

  72. A. Connes and H. Moscovici. Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Topology, 29(3):345–388, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  73. F. X. Connolly and M. O. M. da Silva. The groups Nr K0(Z π) are finitely generated Z[N r ]-modules if π is a finite group. K -Theory, 9(1):1–11, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  74. F. X. Connolly and T. Ko´zniewski. Nil groups in K-theory and surgery theory. Forum Math., 7(1):45–76, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  75. F. X. Connolly and S. Prassidis. On the exponent of the cokernel of the forget-control map on K0-groups. Fund. Math., 172(3):201–216, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  76. F. X. Connolly and S. Prassidis. On the exponent of the NK0-groups of virtually infinite cyclic groups. Canad. Math. Bull., 45(2):180–195, 2002.

    MATH  MathSciNet  Google Scholar 

  77. F. X. Connolly and A. Ranicki. On the calculation of UNIL∗. arXiv:math.AT/0304016v1, 2003.

    Google Scholar 

  78. J. Cuntz. K-theoretic amenability for discrete groups. J. Reine Angew. Math., 344:180–195, 1983.

    MATH  MathSciNet  Google Scholar 

  79. C. W. Curtis and I. Reiner. Methods of representation theory. Vol. II. John Wiley & Sons Inc., New York, 1987. With applications to finite groups and orders, A Wiley-Interscience Publication.

    MATH  Google Scholar 

  80. K. R. Davidson. C ∗ -algebras by example, volume 6 of Fields Institute Monographs. American Mathematical Society, Providence, RI, 1996.

    Google Scholar 

  81. J. F. Davis. Manifold aspects of the Novikov conjecture. In Surveys on surgery theory, Vol. 1, pages 195–224. Princeton Univ. Press, Princeton, NJ, 2000.

    Google Scholar 

  82. J. F. Davis and W. Lück. Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory. K -Theory, 15(3):201–252, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  83. J. F. Davis and W. Lück. The p-chain spectral sequence. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 257, Münster. To appear in a special issue of K -Theory dedicated to H. Bass, 2002.

    Google Scholar 

  84. P. de la Harpe. Groupes hyperboliques, algèbres d’opérateurs et un théorème de Jolissaint. C. R. Acad. Sci. Paris Sér. I Math., 307(14):771–774, 1988.

    MATH  Google Scholar 

  85. R. K. Dennis, M. E. Keating, and M. R. Stein. Lower bounds for the order of K2( G) and Wh2(G). Math. Ann., 223(2):97–103, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  86. S. K. Donaldson. Irrationality and the h-cobordism conjecture. J. Differential Geom., 26(1):141–168, 1987.

    MATH  MathSciNet  Google Scholar 

  87. A. N. Dranishnikov, G. Gong, V. Lafforgue, and G. Yu. Uniform embeddings into Hilbert space and a question of Gromov. Canad. Math. Bull., 45(1):60–70, 2002.

    MATH  MathSciNet  Google Scholar 

  88. E. Dror Farjoun. Homotopy and homology of diagrams of spaces. In Algebraic topology (Seattle, Wash., 1985), pages 93–134. Springer-Verlag, Berlin, 1987.

    Google Scholar 

  89. M. J. Dunwoody. K2(Zπ) for π a group of order two or three. J. London Math. Soc. (2), 11(4):481–490, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  90. W. Dwyer, T. Schick, and S. Stolz. Remarks on a conjecture of Gromov and Lawson. In High-dimensional manifold topology, pages 159–176. World Sci. Publishing, River Edge, NJ, 2003.

    Chapter  Google Scholar 

  91. W. Dwyer, M. Weiss, and B. Williams. A parametrized index theorem for the algebraic K-theory Euler class. Acta Math., 190(1):1–104, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  92. B. Eckmann. Cyclic homology of groups and the Bass conjecture. Comment. Math. Helv., 61(2):193–202, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  93. B. Eckmann. Projective and Hilbert modules over group algebras, and finitely dominated spaces. Comment. Math. Helv., 71(3):453–462, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  94. D.S. Farley. Proper isometric actions of Thompson’s groups on Hilbert space. Int. Math. Res. Not., (45):2409–2414, 2003.

    Article  MathSciNet  Google Scholar 

  95. F. T. Farrell. The nonfiniteness of Nil. Proc. Amer. Math. Soc., 65(2):215–216, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  96. F. T. Farrell. The exponent of UNil. Topology, 18(4):305–312, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  97. F. T. Farrell and W. C. Hsiang. On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds. In Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 1, Proc. Sympos. Pure Math., XXXII, pages 325–337. Amer. Math. Soc., Providence, R.I., 1978.

    Google Scholar 

  98. F.T. Farrell and W.C. Hsiang. The topological-Euclidean space form problem. Invent. Math., 45(2):181–192, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  99. F. T. Farrell and W. C. Hsiang. On Novikov’s conjecture for nonpositively curved manifolds. I. Ann. of Math. (2), 113(1):199–209, 1981.

    Article  MathSciNet  Google Scholar 

  100. F. T. Farrell and W. C. Hsiang. The Whitehead group of poly-(finite or cyclic) groups. J. London Math. Soc. (2), 24(2):308–324, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  101. F. T. Farrell and L. E. Jones. h-cobordisms with foliated control. Bull. Amer. Math. Soc. (N.S.), 15(1):69–72, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  102. F. T. Farrell and L. E. Jones. K-theory and dynamics. I. Ann. of Math. (2), 124(3):531–569, 1986.

    Article  MathSciNet  Google Scholar 

  103. F.T. Farrell and L.E. Jones. Foliated control with hyperbolic leaves. K -Theory, 1(4):337–359, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  104. F. T. Farrell and L. E. Jones. Foliated control theory. I, II. K -Theory, 2(3):357–430, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  105. F. T. Farrell and L. E. Jones. The surgery L-groups of poly-(finite or cyclic) groups. Invent. Math., 91(3):559–586, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  106. F. T. Farrell and L. E. Jones. Negatively curved manifolds with exotic smooth structures. J. Amer. Math. Soc., 2(4):899–908, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  107. F. T. Farrell and L. E. Jones. A topological analogue of Mostow’s rigidity theorem. J. Amer. Math. Soc., 2(2):257–370, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  108. F. T. Farrell and L. E. Jones. Foliated control without radius of injectivity restrictions. Topology, 30(2):117–142, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  109. F. T. Farrell and L. E. Jones. Rigidity in geometry and topology. In Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), pages 653–663, Tokyo, 1991. Math. Soc. Japan.

    Google Scholar 

  110. F. T. Farrell and L. E. Jones. Stable pseudoisotopy spaces of compact nonpositively curved manifolds. J. Differential Geom., 34(3):769–834, 1991.

    MATH  MathSciNet  Google Scholar 

  111. F. T. Farrell and L. E. Jones. Isomorphism conjectures in algebraic K-theory. J. Amer. Math. Soc., 6(2):249–297, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  112. F. T. Farrell and L. E. Jones. Topological rigidity for compact non-positively curved manifolds. In Differential geometry: Riemannian geometry (Los Angeles, CA, 1990), pages 229–274. Amer. Math. Soc., Providence, RI, 1993.

    Google Scholar 

  113. F. T. Farrell and L. E. Jones. The lower algebraic K-theory of virtually infinite cyclic groups. K -Theory, 9(1):13–30, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  114. F. T. Farrell and L. E. Jones. Collapsing foliated Riemannian manifolds. Asian J. Math., 2(3):443–494, 1998.

    MATH  MathSciNet  Google Scholar 

  115. F. T. Farrell and L. E. Jones. Rigidity for aspherical manifolds with π1 ⊂ GLm(R). Asian J. Math., 2(2):215–262, 1998.

    MATH  MathSciNet  Google Scholar 

  116. F. T. Farrell and L. E. Jones. Local collapsing theory. Pacific J. Math., 210(1):1–100, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  117. F. T. Farrell and P. A. Linnell. K-theory of solvable groups. Proc. London Math. Soc. (3), 87(2):309–336, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  118. F. T. Farrell and P. A. Linnell. Whitehead groups and the Bass conjecture. Math. Ann., 326(4):723–757, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  119. F.T. Farrell and S.K. Roushon. The Whitehead groups of braid groups vanish. Internat. Math. Res. Notices, (10):515–526, 2000.

    Google Scholar 

  120. T. Farrell. The Borel conjecture. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 225–298. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 1. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  121. T. Farrell, L. Göttsche, and W. Lück, editors. High dimensional manifold theory. Number 9 in ICTP Lecture Notes. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 1. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  122. T. Farrell, L. Göttsche, and W. Lück, editors. High dimensional manifold theory. Number 9 in ICTP Lecture Notes. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 2. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  123. T. Farrell, L. Jones, and W. Lück. A caveat on the isomorphism conjecture in L-theory. Forum Math., 14(3):413–418, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  124. S. Ferry. The homeomorphism group of a compact Hilbert cube manifold is an anr. Ann. Math. (2), 106(1):101–119, 1977.

    Article  MathSciNet  Google Scholar 

  125. S. Ferry. A simple-homotopy approach to the finiteness obstruction. InShape theory and geometric topology (Dubrovnik, 1981), pages 73–81. Springer-Verlag, Berlin, 1981.

    Google Scholar 

  126. S. Ferry and A. Ranicki. A survey of Wall’s finiteness obstruction. In Surveys on surgery theory, Vol. 2, volume 149 of Ann. of Math. Stud., pages 63–79. Princeton Univ. Press, Princeton, NJ, 2001.

    Google Scholar 

  127. S. C. Ferry, A. A. Ranicki, and J. Rosenberg. A history and survey of the Novikov conjecture. In Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993), pages 7–66. Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

  128. S. C. Ferry, A. A. Ranicki, and J. Rosenberg, editors. Novikov conjectures, index theorems and rigidity. Vol. 1. Cambridge University Press, Cambridge, 1995. Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6–10, 1993.

    Google Scholar 

  129. S. C. Ferry and S. Weinberger. Curvature, tangentiality, and controlled topology. Invent. Math., 105(2):401–414, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  130. Z. Fiedorowicz. The Quillen-Grothendieck construction and extension of pairings. In Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), I, pages 163–169. Springer-Verlag, Berlin, 1978.

    Google Scholar 

  131. M. H. Freedman. The topology of four-dimensional manifolds. J. Differential Geom., 17(3):357–453, 1982.

    MATH  MathSciNet  Google Scholar 

  132. M. H. Freedman. The disk theorem for four-dimensional manifolds. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), pages 647–663, Warsaw, 1984. PWN.

    Google Scholar 

  133. S. M. Gersten. On the spectrum of algebraic K-theory. Bull. Amer. Math. Soc., 78:216–219, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  134. É. Ghys. Groupes al éatoires (d’après Misha Gromov, ... ). Astérisque, (294):viii, 173–204, 2004.

    Google Scholar 

  135. D. Grayson. Higher algebraic K-theory. II (after Daniel Quillen). In Algebraic K -theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976), pages 217–240. Lecture Notes in Math., Vol. 551. Springer-Verlag, Berlin, 1976.

    Google Scholar 

  136. M. Gromov. Large Riemannian manifolds. In Curvature and topology of Riemannian manifolds (Katata, 1985), pages 108–121. Springer-Verlag, Berlin, 1986.

    Google Scholar 

  137. M. Gromov. Asymptotic invariants of infinite groups. In Geometric group theory, Vol. 2 (Sussex, 1991), pages 1–295. Cambridge Univ. Press, Cambridge, 1993.

    Google Scholar 

  138. M. Gromov. Spaces and questions. Geom. Funct. Anal., (Special Volume, Part I):118–161, 2000. GAFA 2000 (Tel Aviv, 1999).

    Google Scholar 

  139. M. Gromov. Random walk in random groups. Geom. Funct. Anal., 13(1):73–146, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  140. E. Guentner, N. Higson, and S. Weinberger. The Novikov conjecture for linear groups. preprint, 2003.

    Google Scholar 

  141. I. Hambleton. Algebraic K- and L-theory and applications to the topology of manifolds. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 299–369. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 1. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  142. I. Hambleton and E. K. Pedersen. Identifying assembly maps in K- and L-theory. Math. Annalen, 328(1):27–58, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  143. I. Hambleton and L. R. Taylor. A guide to the calculation of the surgery obstruction groups for finite groups. In Surveys on surgery theory, Vol. 1, pages 225–274. Princeton Univ. Press, Princeton, NJ, 2000.

    Google Scholar 

  144. A. E. Hatcher. Concordance spaces, higher simple-homotopy theory, and applications. In Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 1, pages 3–21. Amer. Math. Soc., Providence, R.I., 1978.

    Google Scholar 

  145. J.-C. Hausmann. On the homotopy of nonnilpotent spaces. Math. Z., 178(1):115–123, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  146. L. Hesselholt and I. Madsen. On the K-theory of nilpotent endomorphisms. In Homotopy methods in algebraic topology (Boulder, CO, 1999), volume 271 of Contemp. Math., pages 127–140. Amer. Math. Soc., Providence, RI, 2001.

    Google Scholar 

  147. N. Higson. The Baum-Connes conjecture. In Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), pages 637–646 (electronic), 1998.

    Google Scholar 

  148. N. Higson. Bivariant K-theory and the Novikov conjecture. Geom. Funct. Anal., 10(3):563–581, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  149. N. Higson and G. Kasparov. E-theory and KK-theory for groups which act properly and isometrically on Hilbert space. Invent. Math., 144(1):23–74, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  150. N. Higson, V. Lafforgue, and G. Skandalis. Counterexamples to the Baum-Connes conjecture. Geom. Funct. Anal., 12(2):330–354, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  151. N. Higson, E. K. Pedersen, and J. Roe. C ∗-algebras and controlled topology. K -Theory, 11(3):209–239, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  152. N. Higson and J. Roe. On the coarse Baum-Connes conjecture. In Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993), pages 227–254. Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

  153. N. Higson and J. Roe. Amenable group actions and the Novikov conjecture. J. Reine Angew. Math., 519:143–153, 2000.

    MATH  MathSciNet  Google Scholar 

  154. N. Higson and J. Roe. Analytic K -homology. Oxford University Press, Oxford, 2000. Oxford Science Publications.

    MATH  Google Scholar 

  155. B. Hu. Retractions of closed manifolds with nonpositive curvature. In Geometric group theory (Columbus, OH, 1992), volume 3 of Ohio State Univ. Math. Res. Inst. Publ., pages 135–147. de Gruyter, Berlin, 1995.

    Google Scholar 

  156. B. Z. Hu. Whitehead groups of finite polyhedra with nonpositive curvature. J. Differential Geom., 38(3):501–517, 1993.

    MATH  MathSciNet  Google Scholar 

  157. K. Igusa. The stability theorem for smooth pseudoisotopies. K -Theory, 2(1-2):vi+355, 1988.

    Google Scholar 

  158. H. Inassaridze. Algebraic K -theory, volume 311 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1995.

    MATH  Google Scholar 

  159. M. Joachim. K-homology of C ∗-categories and symmetric spectra representing K-homology. Math. Annalen, 328:641–670, 2003.

    Article  MathSciNet  Google Scholar 

  160. E. Jones. A paper for F.T. Farrell on his 60-th birthday. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, pages 200–260. 2003. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001.

    Google Scholar 

  161. L. Jones. A paper for F.T. Farrell on his 60-th birthday. preprint, to appear in the Proceedings of the school/conference on “High-dimensional Manifold Topology” in Trieste, May/June 2001.

    Google Scholar 

  162. L.Jones.Foliatedcontroltheoryanditsapplications.InT.Farrell,L.Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 405–460. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 2. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  163. P. Julg. Remarks on the Baum-Connes conjecture and Kazhdan’s property T. In Operator algebras and their applications (Waterloo, ON, 1994/1995), volume 13 of Fields Inst. Commun., pages 145–153. Amer. Math. Soc., Providence, RI, 1997.

    Google Scholar 

  164. P. Julg. Travaux de N. Higson et G. Kasparov sur la conjecture de Baum-Connes. Astérisque, (252):Exp. No. 841, 4, 151–183, 1998. Séminaire Bourbaki. Vol. 1997/98.

    Google Scholar 

  165. P. Julg. La conjecture de Baum-Connes `a coefficients pour le groupe Sp(n, 1). C. R. Math. Acad. Sci. Paris, 334(7):533–538, 2002.

    MATH  MathSciNet  Google Scholar 

  166. P. Julg and G. Kasparov. Operator K-theory for the group SU(n, 1). J. Reine Angew. Math., 463:99–152, 1995.

    MATH  MathSciNet  Google Scholar 

  167. M. Karoubi. Bott periodicity in topological, algebraic and hermitian K-theory. In this Handbook.

    Google Scholar 

  168. G. Kasparov. Novikov’s conjecture on higher signatures: the operator K-theory approach. In Representation theory of groups and algebras, pages 79–99. Amer. Math. Soc., Providence, RI, 1993.

    Google Scholar 

  169. G. Kasparov and G. Skandalis. Groupes “boliques” et conjecture de Novikov. C. R. Acad. Sci. Paris Sér. I Math., 319(8):815–820, 1994.

    MATH  MathSciNet  Google Scholar 

  170. G. G. Kasparov. Equivariant KK-theory and the Novikov conjecture. Invent. Math., 91(1):147–201, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  171. G. G. Kasparov. K-theory, group C ∗-algebras, and higher signatures (conspectus). In Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993), pages 101–146. Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

  172. G. G. Kasparov and G. Skandalis. Groups acting on buildings, operator K-theory, and Novikov’s conjecture. K -Theory, 4(4):303–337, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  173. M. A. Kervaire. Le théorème de Barden-Mazur-Stallings. Comment. Math. Helv., 40:31–42, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  174. N. Keswani. Homotopy invariance of relative eta-invariants and C ∗-algebra K-theory. Electron. Res. Announc. Amer. Math. Soc., 4:18–26 (electronic), 1998.

    Article  MATH  MathSciNet  Google Scholar 

  175. N. Keswani. Von Neumann eta-invariants and C ∗-algebra K-theory. J. London Math. Soc. (2), 62(3):771–783, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  176. R. C. Kirby and L. C. Siebenmann. Foundational essays on topological manifolds, smoothings, and triangulations. Princeton University Press, Princeton, N.J., 1977. With notes by J. Milnor and M. F. Atiyah, Annals of Mathematics Studies, No. 88.

    MATH  Google Scholar 

  177. M. Kolster. K-theory and arithmetics. Lectures - ICTP Trieste 2002.

    Google Scholar 

  178. M. Kreck. Surgery and duality. Ann. of Math. (2), 149(3):707–754, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  179. M. Kreck and W. Lück. The Novikov Conjecture: Geometry and Algebra, volume 33 of Oberwolfach Seminars. Birkhäuser, 2004.

    Google Scholar 

  180. P. H. Kropholler and G. Mislin. Groups acting on finite-dimensional spaces with finite stabilizers. Comment. Math. Helv., 73(1):122–136, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  181. A. O. Kuku. Kn, SKn of integral group-rings and orders. In Applications of algebraic K -theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), pages 333–338. Amer. Math. Soc., Providence, RI, 1986.

    Google Scholar 

  182. A. O. Kuku and G. Tang. Higher K-theory of group-rings of virtually infinite cyclic groups. Math. Ann., 325(4):711–726, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  183. V. Lafforgue. Une démonstration de la conjecture de Baum-Connes pour les groupes réductifs sur un corps p-adique et pour certains groupes discrets possédant la propriété (T). C. R. Acad. Sci. Paris Sér. I Math., 327(5):439–444, 1998.

    MATH  MathSciNet  Google Scholar 

  184. V. Lafforgue. A proof of property (RD) for cocompact lattices of SL(3, R) and SL(3, C). J. Lie Theory, 10(2):255–267, 2000.

    MATH  MathSciNet  Google Scholar 

  185. V. Lafforgue. Banach KK-theory and the Baum-Connes conjecture. In European Congress of Mathematics, Vol. II (Barcelona, 2000), volume 202 of Progr. Math., pages 31–46. Birkhäuser, Basel, 2001.

    Google Scholar 

  186. V. Lafforgue. K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes. Invent. Math., 149(1):1–95, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  187. T. Y. Lam. A first course in noncommutative rings. Springer-Verlag, New York, 1991.

    MATH  Google Scholar 

  188. E. C. Lance. Hilbert C ∗ -modules. Cambridge University Press, Cambridge, 1995. A toolkit for operator algebraists.

    Book  Google Scholar 

  189. R. Lee and R. H. Szczarba. The group K3(Z) is cyclic of order forty-eight. Ann. of Math. (2), 104(1):31–60, 1976.

    Article  MathSciNet  Google Scholar 

  190. L. G. Lewis, Jr., J. P. May, M. Steinberger, and J. E. McClure. Equivariant stable homotopy theory. Springer-Verlag, Berlin, 1986. With contributions by J. E. McClure.

    MATH  Google Scholar 

  191. P. A. Linnell. Decomposition of augmentation ideals and relation modules. Proc. London Math. Soc. (3), 47(1):83–127, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  192. P. A. Linnell. Division rings and group von Neumann algebras. Forum Math., 5(6):561–576, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  193. E. Lluis-Puebla, J.-L. Loday, H. Gillet, C. Soulé, and V. Snaith. Higher algebraic K -theory: an overview, volume 1491 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1992.

    MATH  Google Scholar 

  194. J.-L. Loday. K-théorie algébrique et représentations de groupes. Ann. Sci. École Norm. Sup. (4), 9(3):309–377, 1976.

    MATH  MathSciNet  Google Scholar 

  195. J. Lott. The zero-in-the-spectrum question. Enseign. Math. (2), 42(3-4):341–376, 1996.

    MATH  MathSciNet  Google Scholar 

  196. W. Lück. The geometric finiteness obstruction. Proc. London Math. Soc. (3), 54(2):367–384, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  197. W. Lück. Transformation groups and algebraic K -theory. Springer-Verlag, Berlin, 1989. Mathematica Gottingensis.

    Google Scholar 

  198. W. Lück. Dimension theory of arbitrary modules over finite von Neumann algebras and L2 -Betti numbers. II. Applications to Grothendieck groups, L2 - Euler characteristics and Burnside groups. J. Reine Angew. Math., 496:213–236, 1998.

    MATH  MathSciNet  Google Scholar 

  199. W. Lück. The type of the classifying space for a family of subgroups. J. Pure Appl. Algebra, 149(2):177–203, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  200. W. Lück. A basic introduction to surgery theory. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 1–224. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 1. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  201. W. Lück. Chern characters for proper equivariant homology theories and applications to K- and L-theory. J. Reine Angew. Math., 543:193–234, 2002.

    MATH  MathSciNet  Google Scholar 

  202. W. Lück. L2 -invariants: theory and applications to geometry and K -theory, volume 44 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Springer-Verlag, Berlin, 2002.

    Google Scholar 

  203. W. Lück. The relation between the Baum-Connes conjecture and the trace conjecture. Invent. Math., 149(1):123–152, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  204. W. Lück. K-and L-theory of the semi-direct product discrete threedimensional Heisenberg group by Z|4. in preparation, 2003.

    Google Scholar 

  205. W. Lück. L2-invariants from the algebraic point of view. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 295, Münster, arXiv:math.GT/0310489 v1, 2003.

    Google Scholar 

  206. W.Lück.Surveyonclassifyingspacesforfamiliesofsubgroups.Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 308, Münster, arXiv:math.GT/0312378 v1, 2004.

    Google Scholar 

  207. W. Lück and D. Meintrup. On the universal space for group actions with compact isotropy. In Geometry and topology: Aarhus (1998), pages 293–305. Amer. Math. Soc., Providence, RI, 2000.

    Google Scholar 

  208. W. Lück, H. Reich, J. Rognes, and M. Varisco. In preparation, 2003.

    Google Scholar 

  209. W. Lück and M. Rørdam. Algebraic K-theory of von Neumann algebras. K -Theory, 7(6):517–536, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  210. W. Lück and T. Schick. Approximating L2 -signatures by their finitedimensional analogues. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 190, Münster, to appear in Forum, 2001.

    Google Scholar 

  211. W. Lück and T. Schick. Various L2 -signatures and a topological L2 -signature theorem. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, pages 200–260. 2003. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001.

    Google Scholar 

  212. W. Lück and R. Stamm. Computations of K- and L-theory of cocompact planar groups. K -Theory, 21(3):249–292, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  213. I. Madsen and M. Rothenberg. Equivariant pseudo-isotopies and K−1. In Transformation groups (Osaka, 1987), volume 1375 of Lecture Notes in Math., pages 216–230. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  214. V. Mathai. Spectral flow, eta invariants, and von Neumann algebras. J. Funct. Anal., 109(2):442–456, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  215. M. Matthey and G. Mislin. Equivariant K-homology and restriction to finite cyclic subgroups. K -Theory, 32(2):167–179, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  216. D. Meintrup. On the Type of the Universal Space for a Family of Subgroups. PhD thesis, Westfälische Wilhelms-Universität Münster, 2000.

    Google Scholar 

  217. D. Meintrup and T. Schick. A model for the universal space for proper actions of a hyperbolic group. New York J. Math., 8:1–7 (electronic), 2002.

    MATH  MathSciNet  Google Scholar 

  218. J. Milnor. On manifolds homeomorphic to the 7-sphere. Ann. of Math. (2), 64:399–405, 1956.

    Article  MathSciNet  Google Scholar 

  219. J. Milnor. Lectures on the h -cobordism theorem. Princeton University Press, Princeton, N.J., 1965.

    MATH  Google Scholar 

  220. J. Milnor. Whitehead torsion. Bull. Amer. Math. Soc., 72:358–426, 1966.

    Article  MATH  MathSciNet  Google Scholar 

  221. J. Milnor. Introduction to algebraic K -theory. Princeton University Press, Princeton, N.J., 1971. Annals of Mathematics Studies, No. 72.

    MATH  Google Scholar 

  222. I. Mineyev and G. Yu. The Baum-Connes conjecture for hyperbolic groups. Invent. Math., 149(1):97–122, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  223. A. S. Miščenko and A. T. Fomenko. The index of elliptic operators over C ∗-algebras. Izv. Akad. Nauk SSSR Ser. Mat., 43(4):831–859, 967, 1979. English translation in Math. USSR-Izv. 15 (1980), no. 1, 87–112.

    Google Scholar 

  224. G. Mislin. Wall’s finiteness obstruction. In Handbook of algebraic topology, pages 1259–1291. North-Holland, Amsterdam, 1995.

    Chapter  Google Scholar 

  225. G. Mislin and A. Valette. Proper group actions and the Baum-Connes Conjecture. Advanced Courses in Mathematics CRM Barcelona. Birkhäuser, 2003.

    Google Scholar 

  226. S. A. Mitchell. On the Lichtenbaum-Quillen conjectures from a stable homotopy-theoretic viewpoint. In Algebraic topology and its applications, volume 27 of Math. Sci. Res. Inst. Publ., pages 163–240. Springer-Verlag, New York, 1994.

    Google Scholar 

  227. J. A. Moody. Brauer induction for G0 of certain infinite groups. J. Algebra, 122(1):1–14, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  228. G. J. Murphy. C ∗ -algebras and operator theory. Academic Press Inc., Boston, MA, 1990.

    Google Scholar 

  229. J. Neukirch, A. Schmidt, and K. Wingberg. Cohomology of number fields. Springer-Verlag, Berlin, 2000.

    MATH  Google Scholar 

  230. A. J. Nicas. On the higher Whitehead groups of a Bieberbach group. Trans. Amer. Math. Soc., 287(2):853–859, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  231. R. Oliver. Projective class groups of integral group rings: a survey. In Orders and their applications (Oberwolfach, 1984), volume 1142 of Lecture Notes in Math., pages 211–232. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  232. R. Oliver. Whitehead groups of finite groups. Cambridge University Press, Cambridge, 1988.

    Book  MATH  Google Scholar 

  233. H. Oyono-Oyono. Baum-Connes Conjecture and extensions. J. Reine Angew. Math., 532:133–149, 2001.

    MATH  MathSciNet  Google Scholar 

  234. H. Oyono-Oyono. Baum-Connes conjecture and group actions on trees. K -Theory, 24(2):115–134, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  235. D. S. Passman. Infinite crossed products. Academic Press Inc., Boston, MA, 1989.

    MATH  Google Scholar 

  236. K. Pearson. Algebraic K-theory of two-dimensional crystallographic groups. K -Theory, 14(3):265–280, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  237. E. Pedersen and C. Weibel. A non-connective delooping of algebraic K-theory. In Algebraic and Geometric Topology; proc. conf. Rutgers Uni., New Brunswick 1983, volume 1126 of Lecture notes in mathematics, pages 166–181. Springer-Verlag, 1985.

    Google Scholar 

  238. E. K. Pedersen. On the K−i-functors. J. Algebra, 90(2):461–475, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  239. E. K. Pedersen. On the bounded and thin h-cobordism theorem parameterized by R k . In Transformation groups, Pozna´n 1985, volume 1217 of Lecture Notes in Math., pages 306–320. Springer-Verlag, Berlin, 1986.

    Chapter  Google Scholar 

  240. E. K. Pedersen. Controlled methods in equivariant topology, a survey. In Current trends in transformation groups, volume 7 of K -Monogr. Math., pages 231–245. Kluwer Acad. Publ., Dordrecht, 2002.

    Google Scholar 

  241. E. K. Pedersen and C. A. Weibel. K-theory homology of spaces. In Algebraic topology (Arcata, CA, 1986), pages 346–361. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  242. G. K. Pedersen. C ∗ -algebras and their automorphism groups. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1979.

    Google Scholar 

  243. M. Pimsner and D. Voiculescu. K-groups of reduced crossed products by free groups. J. Operator Theory, 8(1):131–156, 1982.

    MATH  MathSciNet  Google Scholar 

  244. M. V. Pimsner. KK-groups of crossed products by groups acting on trees. Invent. Math., 86(3):603–634, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  245. R. T. Powers. Simplicity of the C ∗-algebra associated with the free group on two generators. Duke Math. J., 42:151–156, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  246. M. Puschnigg. The Kadison-Kaplansky conjecture for word-hyperbolic groups. Invent. Math., 149(1):153–194, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  247. D. Quillen. On the cohomology and K-theory of the general linear groups over a finite field. Ann. of Math. (2), 96:552–586, 1972.

    Article  MathSciNet  Google Scholar 

  248. D. Quillen. Finite generation of the groups Ki of rings of algebraic integers. In Algebraic K -theory, I: Higher K -theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pages 179–198. Lecture Notes in Math., Vol. 341. Springer-Verlag, Berlin, 1973.

    Google Scholar 

  249. D. Quillen. Higher algebraic K-theory. I. In Algebraic K -theory, I: Higher K -theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pages 85–147. Lecture Notes in Math., Vol. 341. Springer-Verlag, Berlin, 1973.

    Google Scholar 

  250. F. Quinn. Ageometric formulation of surgery. In Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969), pages 500–511. Markham, Chicago, Ill., 1970.

    Google Scholar 

  251. F. Quinn. Ends of maps. I. Ann. of Math. (2), 110(2):275–331, 1979.

    Article  MathSciNet  Google Scholar 

  252. F. Quinn. Ends of maps. II. Invent. Math., 68(3):353–424, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  253. A. Ranicki. Foundations of algebraic surgery. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 491–514. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 2. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  254. A. A. Ranicki. Algebraic L-theory. II. Laurent extensions. Proc. London Math. Soc. (3), 27:126–158, 1973.

    Article  MathSciNet  Google Scholar 

  255. A. A. Ranicki. Algebraic L-theory. III. Twisted Laurent extensions. In Algebraic K-theory, III: Hermitian K-theory and geometric application (Proc. Conf. Seattle Res. Center, Battelle Memorial Inst., 1972), pages 412–463. Lecture Notes in Mathematics, Vol. 343. Springer-Verlag, Berlin, 1973.

    Google Scholar 

  256. A. A. Ranicki. Exact sequences in the algebraic theory of surgery. Princeton University Press, Princeton, N.J., 1981.

    MATH  Google Scholar 

  257. A. A. Ranicki. The algebraic theory of finiteness obstruction. Math. Scand., 57(1):105–126, 1985.

    MATH  MathSciNet  Google Scholar 

  258. A. A. Ranicki. Algebraic L -theory and topological manifolds. Cambridge University Press, Cambridge, 1992.

    MATH  Google Scholar 

  259. A. A. Ranicki. Lower K - and L -theory. Cambridge University Press, Cambridge, 1992.

    Book  MATH  Google Scholar 

  260. A. A. Ranicki. On the Novikov conjecture. In Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993), pages 272–337. Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

  261. H. Reich. L2 -Betti numbers, isomorphism conjectures and noncommutative localization. Preprintreihe SFB 478 – Geometrische Strukturen in der Mathematik, Heft 250, Münster, to appear in the Proceedings of the Workshop on Noncommutative Localization - ICMS Edinburgh, April 2002, 2003.

    Google Scholar 

  262. I. Reiner. Class groups and Picard groups of group rings and orders. pages iv+44, Providence, R. I., 1976. American Mathematical Society. Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics, No. 26.

    Google Scholar 

  263. J. Roe. Index theory, coarse geometry, and topology of manifolds. Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1996.

    Google Scholar 

  264. J. Rognes. K4(Z) is the trivial group. Topology, 39(2):267–281, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  265. J. Rognes and C. Weibel. Two-primary algebraic K-theory of rings of integers in number fields. J. Amer. Math. Soc., 13(1):1–54, 2000. Appendix A by Manfred Kolster.

    Article  MATH  MathSciNet  Google Scholar 

  266. J. Rosenberg. K-theory and geometric topology. In this Handbook.

    Google Scholar 

  267. J. Rosenberg. C ∗-algebras, positive scalar curvature and the Novikov conjecture. III. Topology, 25:319–336, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  268. J. Rosenberg. Algebraic K -theory and its applications. Springer-Verlag, New York, 1994.

    MATH  Google Scholar 

  269. J. Rosenberg. Analytic Novikov for topologists. In Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993), pages 338–372. Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

  270. J. Rosenberg and S. Stolz. A “stable” version of the Gromov-Lawson conjecture. In The ˇCech centennial (Boston, MA, 1993), pages 405–418. Amer. Math. Soc., Providence, RI, 1995.

    Google Scholar 

  271. D. Rosenthal. Splitting with continuous control in algebraic K-theory. K -Theory, 32(2):139–166, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  272. C. P. Rourke and B. J. Sanderson. Introduction to piecewise-linear topology. Springer-Verlag, Berlin, 1982. Reprint.

    MATH  Google Scholar 

  273. L. H. Rowen. Ring theory. Vol. II. Academic Press Inc., Boston, MA, 1988.

    Google Scholar 

  274. R. Roy. The trace conjecture—a counterexample. K -Theory, 17(3):209–213, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  275. R. Roy. A counterexample to questions on the integrality property of virtual signature. Topology Appl., 100(2-3):177–185, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  276. J. Sauer. K-theory for proper smooth actions of totally disconnected groups. Ph.D. thesis, 2002.

    Google Scholar 

  277. T. Schick. Finite group extensions and the Baum-Connes conjecture. in preparation.

    Google Scholar 

  278. T. Schick. A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture. Topology, 37(6):1165–1168, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  279. T. Schick. Operator algebras and topology. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 571–660. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 2. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  280. P. Schneider. Über gewisse Galoiscohomologiegruppen. Math. Z., 168(2):181–205, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  281. H. Schröder. K -theory for real C ∗ -algebras and applications. Longman Scientific & Technical, Harlow, 1993.

    Google Scholar 

  282. J.-P. Serre. Cohomologie des groupes discrets. In Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970), pages 77–169. Ann. of Math. Studies, No. 70. Princeton Univ. Press, Princeton, N.J., 1971.

    Google Scholar 

  283. J.-P. Serre. Linear representations of finite groups. Springer-Verlag, New York, 1977. Translated from the second French edition by Leonard L. Scott, Graduate Texts in Mathematics, Vol. 42.

    MATH  Google Scholar 

  284. J. L. Shaneson. Wall’s surgery obstruction groups for G × Z. Ann. of Math. (2), 90:296–334, 1969.

    Article  MathSciNet  Google Scholar 

  285. W.-X. Shi. Deforming the metric on complete Riemannian manifolds. J. Differential Geom., 30(1):223–301, 1989.

    MATH  MathSciNet  Google Scholar 

  286. J. R. Silvester. Introduction to algebraic K -theory. Chapman & Hall, London, 1981. Chapman and Hall Mathematics Series.

    MATH  Google Scholar 

  287. G. Skandalis. Une notion de nucléarité en K-théorie (d’après J. Cuntz). K -Theory, 1(6):549–573, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  288. G. Skandalis. Progrès récents sur la conjecture de Baum-Connes. Contribution de Vincent Lafforgue. Astérisque, (276):105–135, 2002. Séminaire Bourbaki, Vol. 1999/2000.

    Google Scholar 

  289. G. Skandalis, J. L. Tu, and G. Yu. The coarse Baum-Connes conjecture and groupoids. Topology, 41(4):807–834, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  290. C. Soulé. On higher p-adic regulators. In Algebraic K -theory, Evanston 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980), volume 854 of Lecture Notes in Math., pages 372–401. Springer-Verlag, Berlin, 1981.

    Google Scholar 

  291. C. Soulé. Éléments cyclotomiques en K-théorie. Astérisque, (147-148):225–257, 344, 1987. Journées arithmétiques de Besançon (Besançon, 1985).

    Google Scholar 

  292. V. Srinivas. Algebraic K -theory. Birkhäuser Boston Inc., Boston, MA, 1991.

    MATH  Google Scholar 

  293. C. Stark. Topological rigidity theorems. In R. Daverman and R. Sher, editors, Handbook of Geometric Topology, chapter 20. Elsevier, 2002.

    Google Scholar 

  294. C. W. Stark. Surgery theory and infinite fundamental groups. In Surveys on surgery theory, Vol. 1, volume 145 of Ann. of Math. Stud., pages 275–305. Princeton Univ. Press, Princeton, NJ, 2000.

    Google Scholar 

  295. N. E. Steenrod. A convenient category of topological spaces. Michigan Math. J., 14:133–152, 1967.

    Article  MATH  MathSciNet  Google Scholar 

  296. M. R. Stein. Excision and K2 of group rings. J. Pure Appl. Algebra, 18(2):213–224, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  297. S. Stolz. Manifolds of positive scalar curvature. In T. Farrell, L. Göttsche, and W. Lück, editors, High dimensional manifold theory, number 9 in ICTP Lecture Notes, pages 661–708. Abdus Salam International Centre for Theoretical Physics, Trieste, 2002. Proceedings of the summer school “High dimensional manifold theory” in Trieste May/June 2001, Number 2. http://www.ictp.trieste.it/˜pub_off/lectures/vol9.html.

    Google Scholar 

  298. R. G. Swan. Induced representations and projective modules. Ann. of Math. (2), 71:552–578, 1960.

    Article  MathSciNet  Google Scholar 

  299. R. G. Swan. K -theory of finite groups and orders. Springer-Verlag, Berlin, 1970. Lecture Notes in Mathematics, Vol. 149.

    MATH  Google Scholar 

  300. R. G. Swan. Higher algebraic K-theory. In K -theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992), volume 58 of Proc. Sympos. Pure Math., pages 247–293. Amer. Math. Soc., Providence, RI, 1995.

    Google Scholar 

  301. R. M. Switzer. Algebraic topology–homotopy and homology. Springer-Verlag, New York, 1975. Die Grundlehren der mathematischen Wissenschaften, Band 212.

    MATH  Google Scholar 

  302. R. W. Thomason. Beware the phony multiplication on Quillen’s A−1 A. Proc. Amer. Math. Soc., 80(4):569–573, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  303. T. tom Dieck. Orbittypen und äquivariante Homologie. I. Arch. Math. (Basel), 23:307–317, 1972.

    MATH  MathSciNet  Google Scholar 

  304. T. tom Dieck. Transformation groups. Walter de Gruyter & Co., Berlin, 1987.

    MATH  Google Scholar 

  305. J.-L. Tu. The Baum-Connes conjecture and discrete group actions on trees. K -Theory, 17(4):303–318, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  306. S. Upadhyay. Controlled algebraic K-theory of integral group ring of SL(3, Z). K -Theory, 10(4):413–418, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  307. A. Valette. Introduction to the Baum-Connes conjecture. Birkhäuser Verlag, Basel, 2002. Fromnotes taken by Indira Chatterji, With an appendix by Guido Mislin.

    MATH  Google Scholar 

  308. K. Varadarajan. The finiteness obstruction of C. T. C. Wall. Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons Inc., New York, 1989. A Wiley-Interscience Publication.

    MATH  Google Scholar 

  309. W. Vogell. Algebraic K-theory of spaces, with bounded control. Acta Math., 165(3-4):161–187, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  310. W. Vogell. Boundedly controlled algebraic K-theory of spaces and its linear counterparts. J. Pure Appl. Algebra, 76(2):193–224, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  311. W. Vogell. Continuously controlled A-theory. K -Theory, 9(6):567–576, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  312. J. B. Wagoner. Delooping classifying spaces in algebraic K-theory. Topology, 11:349–370, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  313. F. Waldhausen. Algebraic K-theory of generalized free products. I, II. Ann. of Math. (2), 108(1):135–204, 1978.

    Article  MathSciNet  Google Scholar 

  314. F. Waldhausen. Algebraic K-theory of topological spaces. I. In Algebraic and geometrictopology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 1, Proc. Sympos. Pure Math., XXXII, pages 35–60. Amer. Math. Soc., Providence, R.I., 1978.

    Google Scholar 

  315. F. Waldhausen. Algebraic K-theory of spaces. In Algebraic and geometric topology (New Brunswick, N.J., 1983), pages 318–419. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  316. F. Waldhausen. Algebraic K-theory of spaces, concordance, and stable homotopy theory. In Algebraic topology and algebraic K -theory (Princeton, N.J., 1983), pages 392–417. Princeton Univ. Press, Princeton, NJ, 1987.

    Google Scholar 

  317. C. T. C. Wall. Finiteness conditions for CW-complexes. Ann. of Math. (2), 81:56–69, 1965.

    Article  MathSciNet  Google Scholar 

  318. C. T. C. Wall. Finiteness conditions for CW complexes. II. Proc. Roy. Soc. Ser. A, 295:129–139, 1966.

    Article  MathSciNet  Google Scholar 

  319. C. T. C. Wall. Poincaré complexes. I. Ann. of Math. (2), 86:213–245, 1967.

    Article  MathSciNet  Google Scholar 

  320. C. T. C. Wall. Surgery on compact manifolds. American Mathematical Society, Providence, RI, second edition, 1999. Edited and with a foreword by A. A. Ranicki.

    Google Scholar 

  321. N. E. Wegge-Olsen. K -theory and C ∗ -algebras. The Clarendon Press Oxford University Press, New York, 1993. A friendly approach.

    Google Scholar 

  322. C. Weibel. Algebraic K-theory of rings of integers in local and global fields. In this Handbook.

    Google Scholar 

  323. C. Weibel. An introduction to algebraic K-theory. In preparation, see http://math.rutgers.edu/˜weibel/Kbook.html.

    Google Scholar 

  324. C. A. Weibel. K-theory and analytic isomorphisms. Invent. Math., 61(2):177–197, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  325. C.A.Weibel.Mayer-VietorissequencesandmodulestructuresonNK ∗. In Algebraic K -theory, Evanston 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980), volume 854 of Lecture Notes in Math., pages 466–493. Springer-Verlag, Berlin, 1981.

    Google Scholar 

  326. M. Weiss. Excision and restriction in controlled K-theory. Forum Math., 14(1):85–119, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  327. M. Weiss and B. Williams. Automorphisms of manifolds and algebraic K-theory. I. K -Theory, 1(6):575–626, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  328. M. Weiss and B. Williams. Assembly. In Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993), pages 332–352. Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

  329. M. Weiss and B. Williams. Automorphisms of manifolds. In Surveys on surgery theory, Vol. 2, volume 149 of Ann. of Math. Stud., pages 165–220. Princeton Univ. Press, Princeton, NJ, 2001.

    Google Scholar 

  330. G. W. Whitehead. Elements of homotopy theory. Springer-Verlag, New York, 1978.

    MATH  Google Scholar 

  331. B. Wilking. Rigidity of group actions on solvable Lie groups. Math. Ann., 317(2):195–237, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  332. B. Williams. K-theory and surgery. In this Handbook.

    Google Scholar 

  333. M. Yamasaki. L-groups of crystallographic groups. Invent. Math., 88(3):571–602, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  334. G. Yu. On the coarse baum-connes conjecture. K-theory, 9:199–221, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  335. G. Yu. Localization algebras and the coarse Baum-Connes conjecture. K -Theory, 11(4):307–318, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  336. G. Yu. Asymptotic Fredholm modules, vector bundles with small variation and a nonvanishing theorem for K-theoretic indices. K -Theory, 13(4):331–346, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  337. G. Yu. The Novikov conjecture for groups with finite asymptotic dimension. Ann. of Math. (2), 147(2):325–355, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  338. G. Yu. The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space. Invent. Math., 139(1):201–240, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  339. G. L. Yu. Baum-Connes conjecture and coarse geometry. K -Theory, 9(3):223–231, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  340. G. L. Yu. Coarse Baum-Connes conjecture. K -Theory, 9(3):199–221, 1995.

    Article  MATH  MathSciNet  Google Scholar 

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    Wolfgang Lück & Holger Reich

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Lück, W., Reich, H. (2005). The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory. In: Friedlander, E., Grayson, D. (eds) Handbook of K-Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27855-9_15

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