The Connes-Kasparov conjecture for almost connected groups and for linear p -adic groups

Jérôme Chabert; Siegfried Echterhoff; Ryszard Nest

Publications Mathématiques de l'IHÉS (2003)

  • Volume: 97, page 239-278
  • ISSN: 0073-8301

Abstract

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Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.

How to cite

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Chabert, Jérôme, Echterhoff, Siegfried, and Nest, Ryszard. "The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups." Publications Mathématiques de l'IHÉS 97 (2003): 239-278. <http://eudml.org/doc/104191>.

@article{Chabert2003,
abstract = {Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.},
author = {Chabert, Jérôme, Echterhoff, Siegfried, Nest, Ryszard},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Baum-Connes conjecture; assembly map; -theory; reduced group},
language = {eng},
pages = {239-278},
publisher = {Springer},
title = {The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups},
url = {http://eudml.org/doc/104191},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Chabert, Jérôme
AU - Echterhoff, Siegfried
AU - Nest, Ryszard
TI - The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups
JO - Publications Mathématiques de l'IHÉS
PY - 2003
PB - Springer
VL - 97
SP - 239
EP - 278
AB - Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.
LA - eng
KW - Baum-Connes conjecture; assembly map; -theory; reduced group
UR - http://eudml.org/doc/104191
ER -

References

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