No CrossRef data available.
Article contents
The Bost conjecture, open subgroups and groups acting on trees
Published online by Cambridge University Press: 23 October 2009
Abstract
We prove that the Bost conjecture with C*-algebra coefficients for locally compact Hausdorff groups passes to open subgroups. We also prove that if a locally compact Hausdorff group acts on a tree, then the Bost conjecture with C*-coefficients is true for the group if and only if it is true for the stabilisers of the vertices.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © ISOPP 2009
References
CE01.Chabert, Jérôme and Echterhoff, Siegfried. Permanence properties of the Baum-Connes conjecture. Doc. Math. 6:127–183 (electronic), 2001.CrossRefGoogle Scholar
CEM01.Chabert, Jérôme, Echterhoff, Siegfried, and Meyer, Ralf. Deux remarques sur l'application de Baum-Connes. C. R. Acad. Sci. Paris, 332, Série 1:607–610, 2001.CrossRefGoogle Scholar
CEOO03.Chabert, Jérôme, Echterhoff, Siegfried, and Oyono-Oyono, Hervé. Shapiro's lemma for topological K-theory of groups. Comment. Math. Helv. 78(1):203–225, 2003.CrossRefGoogle Scholar
DG83.Dupré, Maurice J. and Gillette, Richard M.. Banach bundles, Banach modules and automorphisms of C*-algebras. Pitman Books Limited, 1983.Google Scholar
Dix64.Dixmier, Jacques. Les C*-algèbres et leurs représentations. Cahiers Scientifiques, Fasc. XXIX. Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964.Google Scholar
EKQR06.Echterhoff, Siegfried, Kaliszewski, S., Quigg, John, and Raeburn, Iain. A categorical approach to imprimitivity theorems for C*-dynamical systems. Mem. Amer. Math. Soc. 180(850):viii+169, 2006.Google Scholar
FD88.Fell, James M. G. and Doran, Robert S.. Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles. Vol. 1, volume 125 of Pure and Applied Mathematics. Academic Press Inc., Boston, MA, 1988. Basic representation theory of groups and algebras.Google Scholar
JT91.Jensen, Kjeld Knudsen and Thomsen, Klaus. Elements of KK-Theory. Birkhäuser, 1991.CrossRefGoogle Scholar
Laf02.Lafforgue, Vincent. K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes. Invent. Math. 149:1–95, 2002.CrossRefGoogle Scholar
Laf06.Lafforgue, Vincent. K-théorie bivariante pour les algèbres de Banach, groupoïdes et conjecture de Baum-Connes. Avec un appendice d'Hervé Oyono-Oyono. J. Inst. Math. Jussieu, 2006. Published online by Cambridge University Press 28 Nov 2006.Google Scholar
MRW87.Muhly, Paul S., Renault, Jean N., and Williams, Dana P.. Equivalence and isomorphism for groupoid C*-algebras. J. Operator Theory 17(1):3–22, 1987.Google Scholar
OO98.Oyono-Oyono, Hervé. La conjecture de Baum-Connes pour les groupes agissant sur les arbres. PhD thesis, Université Claude Bernard - Lyon 1, 1998.CrossRefGoogle Scholar
Par07a.Paravicini, Walther. Induction for Banach algebras, groupoids and KKban. Journal of K-Theory, same issue.Google Scholar
Par07b.Paravicini, Walther. KK-Theory for Banach Algebras And Proper Groupoids. PhD thesis, Universität Münster, 2007. Persistent identifier: urn:nbn:de:hbz:6- 39599660289.Google Scholar
Par07c.Paravicini, Walther. A Note on Banach C 0(X)-Modules. Münster Journal of Mathematics 1 : 267–278, 2008.Google Scholar
Pim86.Pimsner, Mihai V.. KK-groups of crossed products by groups acting on trees. Invent. Math. 86(3):603–634, 1986.CrossRefGoogle Scholar
Ren80.Renault, Jean N.. A Groupoid Approach to C*-Algebras, volume 793. Springer-Verlag, Berlin, 1980. Lecture Notes in Mathematics.CrossRefGoogle Scholar