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Hermitian K — Theory in topology

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Hermitian K-Theory and Geometric Applications

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References

  1. A. Bak, to appear. (See also a preprint with W. Scharlan, Witt groups of orders and finite groups).

    Google Scholar 

  2. H. Bass. papers in these proceedings.

    Google Scholar 

  3. H. Bass. American Journal of Math., to appear.

    Google Scholar 

  4. H. Bass. L3 of finite abelian groups, to appear.

    Google Scholar 

  5. H. Bass. "Algebraic K-theory", Benjamin, 1968.

    Google Scholar 

  6. H. Bass. The stable structure of quite general linear groups, Bull. Amer. Math. Soc. 70 (1964), 429–433.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Bass. J.W. Milnor, and J.-P. Serre. Solutions of the congruence subgroup problem for SLn (n ⩾ 3) and Sp2n (n ⩾ 2), Publ. IHES No.33 (1967), 59–137.

    Google Scholar 

  8. I. Berstein. A proof of the vanishing of the simply-connected surgery obstruction in the odd-dimensional case, preprint, Cornell University, 1969.

    Google Scholar 

  9. I. Berstein. Some algebraic calculations of Wall groups for Z2 (unpublished).

    Google Scholar 

  10. W. Browder. Homotopy type of differentiable manifolds, In "Coloq. on Alg. Top"., Aarhus notes, 1962, 42–46.

    Google Scholar 

  11. W. Browder. Manifolds with π1=Z, Bull. Amer. Math. Soc. 7] (1966), 238–244.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. Browder. "Surgery on simply-connected manifolds". Springer-Verlag, 1972.

    Google Scholar 

  13. W. Browder and T. Petrie. Diffeomorphisms of manifolds and semi free actions on homotopy spheres. Bull. Amer. Math. Soc. 77 (1971), 160–3.

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Browder, T. Petrie, and C.T.C. Wall. The classification of free actions of cyclic groups of odd order on homotopy spheres, Bull. Amer. Math. Soc. 77 (1971), 455–9.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Cappell. Lecture notes on the splitting theorem, mimeographed, Princeton University. [See also Bull. Amer. Math. Soc. 77(1971), 281–6.

    Article  MathSciNet  Google Scholar 

  16. S. Cappell. Papers in these proceedings.

    Google Scholar 

  17. S. Cappell and J.L. Shaneson. The codimension two placement problem and homology equivalent manifolds, to appear. (See also: Submanifolds group actions and Knots I, II, and Non-locally flat embeddings, smoothings, and group actions. to appear in Bull. A.M.S.).

    Google Scholar 

  18. S. Cappell and J.L. Shaneson. Surgery on 4-manifolds and applications. Comm. Math. Helv. 46(1971), 500–528.

    Article  MathSciNet  MATH  Google Scholar 

  19. F.X. Connolly, a paper in these proceedings.

    Google Scholar 

  20. A. Dress. Induction and Structure theorems for Grothendieck and Witt rings of orthogonal representations of finite groups, Bull. A.M.S., to appear. (See also a paper in these proceedings).

    Google Scholar 

  21. F.T. Farrell. Fibering manifolds over a circle. Indiana Jour. of Math. 21 (1971–2)

    Google Scholar 

  22. F.T. Farrell and W.C. Hsiang. Manifolds with π1=Z ×αG, Amer. J. of Math., to appear (See also B.A.M.S. 74(1968), 548–553).

    Google Scholar 

  23. W.C. Hsiang and J.L. Shaneson. Fake tori, in "Topology of manifolds" (Proceedings of the 1969 Georgia Conference on Topology of Manifolds), Markham Press, 1970, 19–50.

    Google Scholar 

  24. W.C. Hsiang and R. Sharpe. A geometric interpretation of KU2, these proceedings.

    Google Scholar 

  25. M. Karoubi. Developpements recents en K-theorie algebrique to appear.

    Google Scholar 

  26. M. Kervaire. Le theoreme de Barden-Mazur-Stallings. Comm. Math. Helv. 40 (1965), 31–42.

    Article  MathSciNet  MATH  Google Scholar 

  27. M. Kervaire and J.W. Milnor. Groups of homotopy spheres, I, Annals of Math. 77(1963), 5-4-537.

    Google Scholar 

  28. R. Kirby and L.C. Siebenmann. On the triangulation of manifolds and the Hauptvermutung. Bull. Amer. Math. Soc. 75 (1969), 742–749. (See also Notices of the Amer. Math. Soc. 16 (1969), 848).

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Lashof and M. Rothenberg. Triangulation of manifolds I, II, Bull. A.M.S. 75 (1969), 750–757.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Lee. Computation of Wall groups, Topology 10(1971), Yale University, 1971.

    Google Scholar 

  31. R. Lee. The spherical space form problem, preprint, Yale University, 1971.

    Google Scholar 

  32. J. Lees. Immersions and surgeries of topological manifolds, Bull. A.M.S. 75 (1969), 529–534.

    Article  MathSciNet  MATH  Google Scholar 

  33. J. Levine. Invariants of Knot cobordism, Inventiones Math. 8 (1969), 98–110.

    Article  MathSciNet  MATH  Google Scholar 

  34. S. Maumary. Paper in these proceddings.

    Google Scholar 

  35. S. Lopez de Medrano. "Involutions on manifolds", Springer Verlag, 1971.

    Google Scholar 

  36. J.W. Milnor. Whitehead torsion, Bull. A.M.S. 72 (1966), 358–426.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  38. J.W. Milnor. "Lectures on the h-cobordism theorem", Princeton University, 1965.

    Google Scholar 

  39. J. W. Milnor. A procedure for killing the homotopy groups of differentiable manifolds, In "Proc. Symp. in Pure Math. 3 (Differential Geometry), Amer. Math. Soc., 1961, 39–55.

    Google Scholar 

  40. S.P. Novikov. Homotopy equivalent smooth manifolds I, Translations of the Amer. Math. Soc. 48 (1965), 271–396. (Rüssian: Izv. Akad. Nauk. SSSR, Ser. Mat. 28 (2) (1964), 365–474).

    Article  Google Scholar 

  41. S. P. Novikov. Hermitian Analogs of K-theory I, II, Mathematics of the USSR-Izvestia 4(1970), 257–292 and 479–505. (Russian: Tom 34 (1970)).

    Article  Google Scholar 

  42. S.P. Novikov. Pontrjagin classes, the fundamental group, and some problems in stable algebra, In "Essays on Topology and Related Topics. Memoires dedies a Georges de Rham. "Springer 1970, 147–155.

    Google Scholar 

  43. D. S. Passman and T. Petrie. Surgery with coefficients in a field, Ann. of Math. 95 (1972) 385–405.

    Article  MathSciNet  MATH  Google Scholar 

  44. T. Petrie. The Atiyah-Singer invariant, the Wall groups, and the function teX+1/teX-1, Ann. of Math. 92(1970), 174–187.

    Article  MathSciNet  MATH  Google Scholar 

  45. F. Quinn. \(B_{(TOP_n )}\)and the surgery obstruction, Bull. A.M.S. 77 (1971), 596–600.

    Article  MathSciNet  MATH  Google Scholar 

  46. A.A. Ranicki, Algebraic L-theory I., II. Proc. Lond. Math. Soc., (to appear) III. these proceedings.

    Google Scholar 

  47. A. A. Ranicki, Geometric L-theory (to appear).

    Google Scholar 

  48. L.C. Siebenmann. Proceedings of the International Congress of Mathematicians, Nice, 1970, Gauthier-Villiars, 1971.

    Google Scholar 

  49. L.C. Siebenmann. "The obstruction to finding a boundary for an open manifold of dimension greater than five", Ph.D. Thesis, Princeton, 1965.

    Google Scholar 

  50. M. K. Siu. "Computation of Unitary Whitehead groups of cyclic groups", Ph.D. Thesis, Columbia University, 1971.

    Google Scholar 

  51. J.L. Shaneson. Wall's surgery obstruction groups for Z × G, Annals of Math. 90 (1969), 296–334.

    Article  MathSciNet  MATH  Google Scholar 

  52. J.L. Shaneson. Product formulas for Ln(π), Bull. A.M.S. 76 (1970), 787–791.

    Article  MathSciNet  MATH  Google Scholar 

  53. J.L. Shaneson. Non-simply-connected surgery and some results in low dimensional topology, Comm. Math. Helv. 45 (1970), 333–352.

    Article  MathSciNet  MATH  Google Scholar 

  54. R. Sharpe. Surgery on compact manifolds: The bounded even dimensional case, to appear.

    Google Scholar 

  55. R. Sharpe. On the structure of the unitary Steinberg group, to appear.

    Google Scholar 

  56. R. Sharpe. These proceedings.

    Google Scholar 

  57. S. Smale. Generalized Poincare's conjecture in dimensions greater than form. Ann. of Math. 74 (1961), 391–406.

    Article  MathSciNet  MATH  Google Scholar 

  58. S. Smale. On the structure of manifolds. Amer. J. of Math. 84 (1962), 387–399.

    Article  MathSciNet  MATH  Google Scholar 

  59. J. Stallings. The piecewise linear structure of euclidean space, Proc. Camb. Phil. Soc. 58 (1962), 481–488.

    Article  MathSciNet  MATH  Google Scholar 

  60. D. Sullivan. "Geometric Topology seminar notes", Princeton University, 1967.

    Google Scholar 

  61. D. Sullivan. Geometric periodicity and the invariants of manifolds, in "Manifolds-Amsterdam 1970", Springer-Verlag 1971.

    Google Scholar 

  62. L.R. Taylor. These proceedings.

    Google Scholar 

  63. C.T.C. Wall. "Surgery on compact manifolds", Academic Press, 1970.

    Google Scholar 

  64. C.T.C. Wall. Some L groups of finite groups. Bull. A.M.S., to appear.

    Google Scholar 

  65. C.T.C. Wall. Foundations of algebraic L theory, these proceedings.

    Google Scholar 

  66. C.T.C. Wall. Free piecewise linear involutions on spheres Bull. A.M.S. 74 (1968), 554–558.

    Article  MathSciNet  MATH  Google Scholar 

  67. C.T.C. Wall. Surgery of non-simply-connected manifolds. Ann. of Math. 84(1966), 212–276.

    Article  MathSciNet  MATH  Google Scholar 

  68. C.T.C. Wall. Classification of Hermitian forms IV. Global rings, to appear.

    Google Scholar 

  69. F. Waldhausen. Whitehead groups of generalized free products, Preliminary report, mimeographed.

    Google Scholar 

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H. Bass

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Shaneson, J.L. (1973). Hermitian K — Theory in topology. In: Bass, H. (eds) Hermitian K-Theory and Geometric Applications. Lecture Notes in Mathematics, vol 343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061367

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  • DOI: https://doi.org/10.1007/BFb0061367

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