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Finitely summable Fredholm modules over higher rank groups and lattices

Published online by Cambridge University Press:  23 December 2010

Michael Puschnigg
Michael Puschnigg
Affiliation:
Institut de Mathématiques de Luminy, UMR 6206 du CNRS, Université de la Méditerranée, 163, Avenue de Luminy 13288 Marseille, Cedex 9, France, puschnigg@univmed.fr
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Abstract

We give a classification (up to smooth homotopy) of finitely summable Fredholm representations (Fredholm modules) over higher rank groups and lattices. Our results are a direct consequence of work of Bader, Furman, Gelander and Monod on generalizations of Kazhdan's property T for locally compact groups.

Keywords

Fredholm moduleSchatten idealbivariant K-theoryProperty (T)uniformly convex Banach spacehigher rank grouprigidity

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 2 , October 2011 , pp. 223 - 239
Copyright
Copyright © ISOPP 2010

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References

1. Bader, U., Furman, A., Gelander, T., Monod, N., Property (T) and rigidity for actions on Banach spaces, Acta Math. 198 no. 1, 57–105, (2007).CrossRefGoogle Scholar
2. Connes, A., Noncommutative differential geometry, Publ. Math. IHES 62, 41–144, (1985)Google Scholar
3. Connes, A., Noncommutative geometry, Academic Press, (1994)Google Scholar
4. Connes, A., Entire cyclic cohomology of Banach algebras and characters of Thetasummable Fredholm modules, K-theory 1, 519–548, (1988)Google Scholar
5. Connes, A., Compact metric spaces, Fredholm modules and hyperfiniteness, Ergod. Th. and Dyn. Syst. 9, 207–220, (1989)Google Scholar
6. Dixmier, J., Les C*-algèbres et leurs représentations, Gauthier-Villars, (1969)Google Scholar
7. De La Harpe, P., Valette, A., La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque No. 175, (1989)Google Scholar
8. Kasparov, G., Operator K-functor and extensions of C*-algebras, Izv. Akad. Nauk. CCCP Ser. Math. 44, 571–636, (1980)Google Scholar
9. Kasparov, G., Equivariant KK-theory and the Novikov conjecture, Invent. Math. 91, 147–201, (1988)CrossRefGoogle Scholar
10. Lindenstrauss, J., Tzafriri, L., Classical Banach spaces I, II, Springer (1977)Google Scholar
11. Margulis, G., Discrete subgroups of semisimple Lie groups, Springer (1991)Google Scholar
12. Nistor, V., A bivariant Chern-Connes character, Ann. of Math. 138, 555–590, (1993)CrossRefGoogle Scholar
13. Puschnigg, M., Diffeotopy functors of ind-algebras and local cyclic cohomology, Docum. Math. J. 8, 143–245, (2003)Google Scholar
14. Raynaud, Y., On ultrapowers of non commutative Lp-spaces, J. Operator. Theory 48, 41–68, (2002)Google Scholar
15. Simon, B., Trace ideals and their applications, LMS Lecture Notes 35, Cambridge University Press (1979)Google Scholar
16. Wang, S.P., On isolated points in the dual spaces of locally compact groups, Math. Ann. 218, 19–35, (1975)Google Scholar