Noncommutative Poincaré Duality for Boundary Actions of Hyperbolic Groups
نویسنده
چکیده
For a large class of word hyperbolic groups Γ the cross product C∗-algebras C(∂Γ)⋊Γ, where ∂Γ denotes the Gromov boundary of Γ satisfy Poincaré duality in K-theory. This class strictly contains fundamental groups of compact, negatively curved manifolds. We discuss the general notion of Poincaré duality for C∗-algebras, construct the fundamental classes for the aforementioned algebras, and prove that KK-products with these classes induce inverse isomorphisms. The Baum-Connes Conjecture for amenable groupoids is used in a crucial way.
منابع مشابه
The Baum-connes Conjecture, Noncommutative Poincaré Duality and the Boundary of the Free Group
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