The Kadison-Kaplansky conjecture for word-hyperbolic groups

Inventiones Mathematicae

Volumn 149, Issue 1, 2002, Pages 153-194

  Puschnigg, Michael ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036988223     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220200216     Document Type: Article

References (35)

1. [AS] M.F. Atiyah, I.M. Singer, The index of elliptic operators I, Annals of Math. 87 (1968), 484-530
2. [At] M.F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Astérisque 32/33 (1976), 43-72
3. [BC] P. Baum, A. Connes, Geometric K-theory for Lie groups and foliations, IHES Preprint, (1982), in Enseignement Math. 46 (2000), 3-42
4. [BCH] P. Baum, A. Connes, N. Higson, Classifying space for proper actions and K-theory of group C*-algebras, Contemp. Math. AMS 167 (1994), 241-291
5. [Bo] J.B. Bost, Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs, Invent. Math. 101 (1990), 261-333
6. [Bu] D. Burghelea, The cyclic homology of group rings, Comment. Math. Helv. 60 (1985), 354-365
7. [Co] A. Connes, Noncommutative Differential Geometry, Publ. Math. IHES 62 (1985), 41-144
8. [Co1] A. Connes, Noncommutative geometry, Academic Press, (1994), 661 pp.
9. [Co2] A. Connes, Entire cyclic cohomology of Banach algebras and characters of Thetasummable Fredholm modules, K-Theory 1 (1988), 519-548
10. [CM] A. Connes, H. Moscovici, Cyclic Cohomology, the Novikov Conjecture and Hyperbolic Groups, Topology 29 (1990), 345-388
11. [Cu] J. Cuntz, A new look at KK-theory, K-theory 1 (1987), 31-51
12. [Cu1] J. Cuntz, Bivariante K-Theorie für lokalkonvexe Algebren und der Chern-Connes Charakter, Docum. Math. J. DMV 2 (1997), 139-182
13. [CQ] J. Cuntz, D. Quillen, Excision in bivariant periodic cyclic cohomology, Invent. Math. 127 (1997), 67-98
14. [CQ1] J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, Journal of the AMS 8(2) (1995), 251-289
15. [Gr] M. Gromov, Hyperbolic groups, in Essays in group theory, MSRI Publ. 8, Springer (1987), 75-263
16. [Hi] N. Higson, A characterization of KK-theory, Pacific J.Math. 126 (1987), 253-276
17. [HK] N. Higson, G. Kasparov, Operator K-theory for groups which act properly and isometrically on Hilbert space, E.R.A. Amer. Math. Soc. 3 (1997), 141-152
18. [HK1] N. Higson, G. Kasparov, E-theory and KK-theory for groups which act properly and isometrically on Hilbert space, Invent. Math. 144 (2001), 23-74
19. [Jol] P. Jolissaint, Rapidly decreasing functions in reduced C*-algebras of groups, Transactions of the AMS 317 (1990), 167-196
20. [Ka] G. Kasparov, Operator K-functor and extensions of C*-algebras, Izv. Akad. Nauk. CCCP Ser. Math. 44 (1980), 571-636
21. [Ka1] G. Kasparov, K-theory, group C*-algebras and higher signatures, Conspectus, (1981), in Novikov Conjectures, Index Theorems and Rigidity, S. Ferry, A. Ranicki, J. Rosenberg, editors, LMS Lecture Notes 226 (1995), 101-146
22. [Ka2] G. Kasparov, Equivariant KK-Theory and the Novikov Conjecture, Invent. Math. 91 (1988), 147-201
23. [KS] G. Kasparov, G. Skandalis, Groupes boliques et conjecture de Novikov, C.R.A.S. 319 (1994), 815-820
24. [KS1] G. Kasparov, G. Skandalis, Groups acting properly on bolic spaces and the Novikov conjecture, Preprint, (2001), 38 pp.
25. [La] V. Lafforgue, K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes, Invent. math. 149 (2002), 1-95
26. [MY] I. Mineyev, G. Yu, The Baum-Connes conjecture for hyperbolic groups, Invent. math. 149 (2002), 97-122
27. [Ni] V. Nistor, Group cohomology and the cyclic cohomology of crossed products, Invent. Math. 99 (1990), 411-423
28. [PV] M. Pimsner, D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain crossed product C*-algebras, J. Operator Theory 4 (1980), 93-118
29. [Pu] M. Puschnigg, Asymptotic Cyclic Cohomology, Springer Lecture Notes 1642, (1996), 238 pp.
30. [Pu1] M. Puschnigg, Cyclic homology theories for topological algebras, K-theory preprint archives 292 (1998), 47 pp.
31. [Pu2] M. Puschnigg, Excision in cyclic homology theories, Invent. Math. 143 (2001), 249-323
32. [Pu3] M. Puschnigg, Local cyclic cohomology of group Banach algebras and the bivariant Chern-Connes character of the gamma element, K-theory preprint archives 356 (1999), 65 pp.
33. [Si] I.M. Singer, Some remarks on operator theory and index theory, in K-Theory and Operator Algebras, Springer Lecture Notes 575 (1977), 128-138
34. [Sk] G. Skandalis, Une notion de nucléarité en K-théorie, K-Theory 1 (1988), 549-573
35. [Th] K. Thomsen, The universal property of equivariant KK-theory, J. Reine Angew. Math. 504 (1998), 55-71