References
[Ab] Abels, H.:Parallelizability of proper actions, globalK-slices and maximal compact subgroups. Math. Ann.212, 1–19 (1974)
[AS1] Atiyah, M.F., Singer, I.M.: The index of elliptic operators. I. Ann. Math.87, 484–530 (1968)
[AS2] Atiyah, M.F., Singer, I.M.: The index of elliptic operators. III. Ann. Math.87, 546–604 (1968)
[BJ] Baaj, S., Julg, P.: Théorie bivariante de Kasparov et opérateurs non bornés dans lesC *-modules hilbertiens. C.R. Acad. Sci. Paris296, 875–878 (1983)
[B1] Blackadar, B.:K-theory for operator algebras. The University of Nevada (Preprint 1985)
[Bo 1] Bourbaki, N.: Topologie générale, ch. III–IV. Paris: Hermann 1960
[Bo 2] Bourbaki, N.: Intégration, ch. VII–VIII. Paris: Hermann 1963
[Ca] Cappell, S.E.: On homotopy invariance of higher signatures. Invent. Math.33, 171–179 (1976)
[CMW] Curto, R.E., Muhly, P.S., Williams, D.P.: Cross products of strongly Morita equivalentC *-algebras. Proc. Am. Math. Soc.90, 528–530 (1984)
[CS] Connes, A., Skandalis, G.: The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. Kyoto Univ.20, 1139–1183 (1984)
[Fa] Fack, T.: Sur la conjecture de Novikov. Publ. Math. Univ. Pierre et Marie Curie vol. 77 (1985)
[FH] Farrell, F.T., Hsiang, W.C.: On Novikov's conjecture for non-positively curved manifolds. I. Ann. Math.113, 199–209 (1981)
[G1] Glushkov, V.M.: The structure of locally bicompact groups and the fifth Hilbert problem. Usp. Matem. Nauk12, No 2, 3–41 (1957)
[Gr 1] Green, P.:C *-algebras of transformation groups with smooth orbit space. Pacif. J. Math.72, 71–97 (1977)
[Gr 2] Green, P.: The structure of imprimitivity algebras. J. Funct. Anal.36, 88–104 (1980)
[He] Helgason, S.: Differential geometry and symmetric spaces. New York London: Academic Press 1962
[Ho] Hochschild, G.: The structure of Lie groups. San Francisco: Holden-Day 1965
[HR] Hsiang, W.C., Rees, H.D.: Miscenko's work on Novikov's conjecture. Contemp. Math.10, 77–98 (1982)
[Hu] Husemoller, D.: Fibre bundles. New York St. Louis San Francisco Toronto London Sydney: McGraw-Hill Book Company 1966
[Ju] Julg, P.:K-théorie équivariante et produits croisés. C.R. Acad. Sci. Paris292, 629–632 (1981)
[JV] Julg, P., Valette, A.:K-theoretic amenability for SL2(Q p ), and the action on the associated tree. J. Funct. Anal.58, 194–215 (1984)
[Ka 1] Kasparov, G.G.: Generalized index of elliptic operators. Funkc. Anal. i Pril.7, No 3, 82–83 (1973)
[Ka 2] Kasparov, G.G.: Topological invariants of elliptic operators. I.K-homology. Izv. Akad. Nauk SSSR, Ser. Mat.39, 796–838 (1975)
[Ka 3] Kasparov, G.G.: HilbertC *-modules: theorems of Stinespring and Voiculescu. J. Oper. Theory4, 133–150 (1980)
[Ka 4] Kasparov, G.G.: The operatorK-functor and extensions ofC *-algebras. Izv. Akad. Nauk SSSR, Ser. Mat.44, 571–636 (1980)
[Ka 5] Kasparov, G.G.:K-theory, groupC *-algebras, and higher signatures (conspectus). Parts 1, 2. The Institute of Chemical Physics (Preprint 1981)
[Ka 6] Kasparov, G.G.: Lorentz groups:K-theory of unitary representations and crossed products. Dokl. Akad. Nauk SSSR275, 541–545 (1984)
[Ka 7] Kasparov, G.G.: OperatorK-theory and its applications: elliptic operators, group representations, higher signatures,C *-extensions. In: Proceedings ICM, Aug. 16–24, 1983 Warszawa, pp. 987–1000. Warsaw-Amsterdam: PWN-Elsevier Publishers 1984
[Ka 8] Kasparov, G.G.: OperatorK-theory and its applications. In: Itogi Nauki i Tekhn., Ser. Sovrem. Probl. Mat. vol. 27, pp. 3–31. Moscow: VINITI 1985
[KM] Kaminker, J., Miller, J.G.: Homotopy invariance of the analytic index of signature operators overC *-algebras. J. Oper. Theory14, 113–127 (1985)
[Mil] Milnor, J.: Morse theory. Princeton: Princeton University Press 1963
[Mis 1] Mishchenko, A.S.: Infinite dimensional representations of discrete groups and higher signatures. Izv. Akad. SSSR, Ser. Mat.38, 81–106 (1974)
[Mis 2] Mishchenko, A.S.:C *-algebras andK-theory. (Lect. Notes Math., vol. 763, pp. 262–274) Berlin Heidelberg New York: Springer 1979
[ML] MacLane, S.: Homology. Berlin Göttingen Heidelberg. Springer 1963
[MP] Mingo, J.A., Phillips, W.J.: Equivariant triviality theorems for HilbertC *-modules. Proc. Am. Math. Soc.91, 225–230 (1984)
[MS] Mishchenko, A.S., Solov'jev, Yu.P.: Representations of Banach algebras and Hirzebruch type formulae. Mat. Sbornic111, 209–226 (1980)
[MZ] Montgomery, D., Zippin, L.: Topological transformation groups. New York: Interscience 1955
[Pe] Pedersen, G.K.:C *-algebras and their automorphism groups. London New York San Francisco: Academic Press 1979
[Pi] Pimsner, M.V.:KK-groups of crossed products by groups acting on trees. Invent. Math.86, 603–634 (1986)
[PV 1] Pimsner, M., Voiculescu, D.: Exact sequences forK-groups and Ext-groups of certain cross-productC *-algebras. J. Oper. Theory4, 93–118 (1980)
[PV 2] Pimsner, M., Voiculescu, D.:K-groups of reduced crossed products by free groups. J. Oper. Theory8, 131–156 (1982)
[Ra] Raghunathan, M.S.: Discrete subgroups of Lie groups. Berlin Heidelberg New York: Springer 1972
[Re] Rees, H.D.: Special manifolds and Novikov's conjecture. Topology22, 365–378 (1983)
[Ri 1] Rieffel, M.A.: Induced representations ofC *-algebras. Adv. Math.13, 176–257 (1974)
[Ri 2] Rieffel, M.A.: Applications of strong Morita equivalence to transformation groupC *-algebras. In: Proc. Symp. Pure Math., vol. 38, Part 1, pp. 299–310. Providence R.I.: Am. Math. Soc. 1982
[Ro] Rosenberg, J.:C *-algebras, positive scalar curvature, and the Novikov conjecture. Publ. Math. Inst. Hautes Etud. Sci.58, 197–212 (1983)
[RS] Rosenberg, J., Schochet, C.: The Künneth theorem and the universal coefficient theorem for Kasparov's generalizedK-functor. Duke Math. J.55, 431–474 (1987)
[Sa] Sakai, S.:C *-algebras andW *-algebras. New York Heidelberg Berlin: Springer 1971
[Sc] Schochet, C.: Topological methods forC *-algebras. I. Spectral sequences. Pacif. J. Math.96, 193–211 (1981)
[Se] Segal, G.: Fredholm complexes. Q. J. Math.21, 385–402 (1970)
[Sk 1] Skandalis, G.: Some remarks on Kasparov theory. J. Funct. Anal.56, 337–347 (1984)
[Sk 2] Skandalis, G.: Exact sequences for the Kasparov groups of graded algebras. Can. J. Math.37, 193–216 (1985)
[SSL] Séminaire “Sophus Lie” 1954/55. Théorie des algébres de Lie. Topologie des groupes de Lie. Paris: Ec. Norm. Supér. 1955
[Wo] Wolf, J.A.: Essential self-adjointness for the Dirac operator and its square. Indiana Univ. Math. J.22, 611–640 (1973)
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Kasparov, G.G. EquivariantKK-theory and the Novikov conjecture. Invent Math 91, 147–201 (1988). https://doi.org/10.1007/BF01404917
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DOI: https://doi.org/10.1007/BF01404917