The Baum-connes Conjecture, Noncommutative Poincaré Duality and the Boundary of the Free Group
نویسنده
چکیده
For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra we construct a canonical K-homology class, which induces a Poincaré duality map K∗(C(∂Γ)⋊Γ) → K (C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case of Γ = F2 the free group on two generators. We point out a direct connection between our constructions and the Baum-Connes Conjecture and eventually use the latter to deduce our result. 2000 Mathematics Subject Classification 46L80
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Noncommutative Poincaré Duality for Boundary Actions of Hyperbolic Groups
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