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arXiv · 0907.2066

A Geometric Description of Equivariant K-Homology for Proper Actions

Paul Baum·Nigel Higson·Thomas Schick
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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.

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Paul Baum, Nigel Higson, Thomas Schick. 2009-07-12. A Geometric Description of Equivariant K-Homology for Proper Actions. https://arxiv.org/abs/0907.2066

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