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Noncommutative Poincare duality for boundary actions of hyperbolic groups

Heath Emerson
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Abstract

For a large class of word hyperbolic groups G the cross product C^*-algebra arising from the action of G on its Gromov boundary is shown to satisfy Poincare duality in K-theory. This class strictly contains fundamental groups of compact, negatively curved manifolds. The Baum-Connes Conjecture for amenable groupoids is used in a crucial way.

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Heath Emerson. 2004-05-20. Noncommutative Poincare duality for boundary actions of hyperbolic groups. https://arxiv.org/abs/math/0405387

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