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The Baum-Connes conjecture, noncommutative Poincare duality and the boundary of the free Group

Heath Emerson
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Abstract

Every hyperbolic group acts continuously on its Gromov boundary. One can form the corresponding cross-product C*-algebra A. We show that there always exists a canonical Poincare duality map from the K-theory of A to the K-homology of A. We show that this map is an isomorphism when the group in question is the free group on two generators. There is a direct connection between our constructions and the Baum-Connes Conjecture, and we use the latter to deduce our result.

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Heath Emerson. 2010-09-27. The Baum-Connes conjecture, noncommutative Poincare duality and the boundary of the free Group. https://arxiv.org/abs/math/0405414

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