A Geometric Description of Equivariant K-Homology for Proper Actions

Abstract

Let G be a discrete group and let X be a G-finite, proper G-CW-complex. We prove that Kasparov's equivariant K-homology groups KK^G(C_0(X),\C) are isomorphic to the geometric equivariant K-homology groups of X that are obtained by making the geometric K-homology theory of Baum and Douglas equivariant in the natural way. This reconciles the original and current formulations of the Baum-Connes conjecture for discrete groups.

33 pages, 1 figure, pdflatex

References in corpus (2)

• On the Equivalence of Geometric and Analytic K-Homology
• Bivariant K-theory via correspondences

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