A new description of equivariant cohomology for totally disconnected groups

2004/12/07 by Christian Voigt, Voigt, Christian
Mathematics · #19D55 #55N91 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:19D55 #msc:55N91

paper · pdf · doi:10.48550/arxiv.math/0412131

30 pages

arxiv created 2004/12/07 · arxiv updated 2009/12/01

Abstract

We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology. This provides a new approach to the construction of Baum and Schneider as well as a computation of equivariant periodic cyclic homology for a natural class of examples. In addition we discuss the relation between cosheaf homology and equivariant Bredon homology. Since the theory of Baum and Schneider generalizes cosheaf homology we finally see that all these approaches to equivariant cohomology for totally disconnected groups are closely related.

Related

• Equivariant local cyclic homology and the equivariant Chern-Connes character
• Chern character for totally disconnected groups
• Equivariant periodic cyclic homology
• An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson
• Orbifold Cohomology as Periodic Cyclic Homology