Approche de la conjecture de Novikov par la cohomologie cyclique [d'après A. Connes, M. Gromov et H. Moscovici]

Skandalis, Georges

Séminaire Bourbaki : volume 1990/91, exposés 730-744, Astérisque, no. 201-202-203 (1991), Exposé no. 739, 22 p.

[1] M. F. Atiyah - Elliptic operators discrete groups and von Neumann algebras, Astérisque 32-33 (1976), 43-72. | Zbl | MR | Numdam

[2] P. Baum and A. Connes - Geometric $K$-theory for Lie groups and foliations, preprint I.H.E.S. (1982). | MR

[3] P. Baum and A. Connes - Leafwise homotopy equivalence and rational Pontrjagin classes. in Foliations, Advanced Studies in Pure Mathematics 5 (1985), 1-14. | Zbl | MR

[4] M. Bökstedt, W. C. Hsiang et I. Madsen - En préparation. Voir l'exposé de BÖKSTEDT au Congrès (ICM) de Kyoto (1990).

[5] J.-B. Bost - $K$-théorie des produits croisés et principe d'Oka, C.R.A.S. Paris 301, Ser. I (1985), n° 5, 189-192. | Zbl | MR

[6] D. Burghelea - The cyclic homology of groups, Comment. Math. Helvetici 60 (1985), 354-365. | Zbl | MR

[7] S. E. Cappell - On homotopy invariance of higher signatures, Invent. Math. 33 (1976), 171-179. | Zbl | MR

[8] P. Cartier - Homologie cyclique : Rapport sur des travaux récents de Connes, Karoubi, Loday, Quillen, ..., Sém. Bourbaki, Février 1984, exposé n° 621, Astérisque 121-122 (1985), 123-146. | Zbl | MR | Numdam

[9] A. Connes - Non commutative differential geometry. Chapter I : The Chern character in $K$-homology. Chapter II : De Rham homology and non commutative algebra, Publ. Math. I.H.E.S. 62 (1986), 257-360. | Zbl | MR | Numdam

[10] A. Connes - Cyclic cohomology and the transverse fundamental class of a foliation, in Geometric methods in operator algebras. H. Araki and E.G. Effros éd., Pitnam Research Notes in Math. Series 123, Longman Wiley (1986), 52-144. | Zbl | MR

[11] A. Connes - Entire cyclic cohomology of Banach algebras and the character of θ-summable Fredholm modules, K-theory 1 (1988), 519- 548. | Zbl

[12] A. Connes, M. Gromov et H. Moscovici - Conjecture de Novikov et fibrés presque plats, C.R.A.S. Paris 310 Ser. I (1990), 273-277. | Zbl | MR

[13] A. Connes and H. Moscovici - Cyclic cohomology, the Novikov | Zbl

conjecture and fundamental groups, Topology 29 (1990), 345-388. | MR

[14] T. Fack - $K$-théorie bivariante de Kasparov, Sém. Bourbaki Février 1983, exposé n° 605, Astérisque 105-106 (1983), 149-166. | Zbl | MR | Numdam | EuDML

[15] F. T. Farrell et W. C. Hsiang - On Novikov's conjecture for nonpositively curved manifolds. I, Ann. Math. 113 (1981), 199-209. | Zbl | MR

[16] B. L. Feigin et B. L. Tsygan - Additive $K$-theory | Zbl

[17] E. Getzler - Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys. 92 (1983), 163-176. | Zbl | MR

[18] É. Ghys - L'invariant de Godbillon-Vey, Sém. Bourbaki, mars 1989, Exposé n° 706, Astérisque 177-178 (1989), 155-182. | Zbl | MR | Numdam | EuDML

[19] É. Ghys - Les groupes hyperboliques, Sém. Bourbaki Mars 1990, exposé n° 722, à paraître dans Astérisque 189-190. | Zbl | MR | Numdam | EuDML

[20] M. Gromov - Hyperbolic groups, in Essays in group theory. M.S.R.I. Publ. 8 (1987), 75-263. | Zbl | MR

[21] M. Gromov et H. B. Lawson - Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I.H.E.S. 58 (1983), 83-196. | Zbl | MR | Numdam | EuDML

[22] P. De La Harpe - Groupes hyperboliques, algèbres d'opérateurs et un théorème de Jolissaint, C.R.A.S. Paris 307 Ser. I (1988), 771-774. | Zbl | MR

[23] M. Hilsum et G. Skandalis - Invariance par homotopie de la signature à coefficients dans un fibré presque plat (d'après Connes-Gromov-Moscovici), à paraître dans J. für Crelle und Ang. Math. | Zbl | EuDML

[24] F. Hirzebruch - Topological methods in algebraic geometry, Berlin-Heidelberg-New York, Springer (1965). | Zbl | MR

[25] W. C. Hsiang, H. D. Rees - Miscenko's work on Novikov's conjecture, Contemp. Math. 72 (1982), 77-98. | Zbl | MR

[26] P. Jolissaint - $K$-groups of reduced $C^{*}$-algebras and rapidly decreasing functions on groups, $K$-theory 2 (1989), 723-735. | Zbl | MR

[27] J. Kaminker and J. G. Miller - Homotopy invariance of the analytic signature operators over $C^{*}$-algebras, J. Operator Theory 14 (1985), 113-127. | Zbl | MR

[28] M. Karoubi - $K$-theory, an introduction, Grund. des Mat. Wis., Springer-Verlag (1978). | Zbl | MR

[29] G. G. Kasparov - Topological invariants of elliptic operators I : $K$-homology, Izv. Akad. Nauk. S.S.S.R. Ser. Mat. 39 (1975), 796-838 ; English transl. in Math. U.S.S.R. Izv. 9 (1975), 751-792. | Zbl | MR

[30] G. G. Kasparov - Equivariant $KK$-theory and the Novikov conjecture, Inv. Math. 91 (1988), 147-201 ; (cf. aussi : $K$-theory, group $C^\ast$-algebras and higher signatures, Conspectus Parts 1 and 2, preprint Chernogolovka (1981). | Zbl | MR | EuDML

[31] G. G. Kasparov - Operator $K$-theory and its applications : elliptic operators, group representations, higher signatures, $C^\ast$-extensions, in Proc. I.C.M. conf. Warsaw 1983, PWN Elsevier (1984), 987-1000. | Zbl | MR

[32] G. G. Kasparov and G. Skandalis - Groups acting on buildings, Operator $K$-theory and Novikov's conjecture, $K$-theory 4 (1991), 303- 337. | Zbl | MR

[33] G. Lusztig - Novikov's higher signature and families of elliptic operators, J. of Diff. Geometry 7 (1971), 229-256. | Zbl | MR

[34] A. S. Mishchenko - Homotopy invariance of non simply connected manifolds, I : Rational invariance, Math. U.S.S.R. Izv. 4 (1970), 509- 519, traduit de Izv. Akad. Nauk. S.S.S.R. Ser. Math. 34 (1970), 501-514. | Zbl | MR

[35] A. S. Mishchenko - Infinite dimensional representations of discrete groups and higher signatures, Izv. Akad. S.S.S.R. Ser. Mat. 38 (1974), 81-106. | Zbl | MR

[36] A. S. Mishchenko - $C^{*}$-algebras and $K$-theory, Springer Lect. Notes in Math. vol. 763 (1979), 262-274. | Zbl | MR

[37] A. S. Mishchenko and Yu. P. Solov'Jev - Représentations of Banach algebras and Hirzebruch type formulae, Mat. Sbornic 111 (1980), 209-226. | Zbl | MR

[38] H. Moscovici - Cyclic cohomology and invariants of non-simply connected manifolds, Proc. I.C.M. Kyoto (1990), à paraître. | Zbl

[39] S. P. Novikov - Analogues hermitiens de la $K$-théorie, Actes, Congrès Intern. Math. 2 (1970), 39-45. | Zbl | MR

[40] M. Pimsner - $KK$-groups of crossed products by groups acting on trees, Inv. Math. 86 (1986), 603-634. | Zbl | MR | EuDML

[41] H. D. Rees - Special manifolds and Novikov's conjecture, Topology 22(1983), 365-378. | Zbl | MR

[42] J. Rosenberg - $C^{*}$-algebras, positive scalar curvature and the Novikov conjecture, Publ. Math. I.H.E.S. 58 (1983), 409-424. | Zbl | MR | Numdam | EuDML

[43] Yu. P. Solov'Ev - Uspekhi Matem. Nauk. 31 n° 1 (1976), 261-262. | Zbl

[44] Yu. P. Solov'Ev - Thèse. Université de Moscou (1976).

[45] S. Weinberger - Aspects of the Novikov conjecture, Contemp. Math. 105 (1990), 281-297. | Zbl | MR