Chern character for totally disconnected groups

2006/08/25 by Christian Voigt, Voigt, Christian · 3 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math.KT #msc:19D55 #msc:19L47 #msc:46L80 #msc:55N91

paper · pdf · doi:10.48550/arxiv.math/0608626

27 pages

arxiv created 2006/08/25 · arxiv updated 2009/12/01

Abstract

In this paper we construct a bivariant Chern character for the equivariant KK-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes conjecture for a totally disconnected group is isomorphic to cosheaf homology. Moreover, it is shown that our transformation extends the Chern character defined by Baum and Schneider for profinite groups.

Cited by

• Periodic cyclic homology of affine Hecke algebras
• Chern character for torsion-free ample groupoids
• Equivariant periodic cyclic homology for ample groupoids

Related

• Chern character, Hopf algebras, and BRS cohomology
• Equivariant local cyclic homology and the equivariant Chern-Connes character
• A new description of equivariant cohomology for totally disconnected groups
• Notes on the Chern-character
• A universal characterization of the Chern character maps