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

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

2004-05-21

arxiv.org/abs/math/0405414v2

IJMMS 2003:38, pp. 2425-2445, (2003)

Mathematics

K-Theory and Homology

Scientific paper

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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