A Geometric Description of Equivariant K-Homology for Proper Actions

Details A Geometric Description of Equivariant K-Homology for Proper Actions A Geometric Description of Equivariant K-Homology for Proper Actions

2009-07-12

arxiv.org/abs/0907.2066v1

Mathematics

K-Theory and Homology

33 pages, 1 figure, pdflatex

Scientific paper

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.

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