Noncommutative Poincaré duality for boundary actions of hyperbolic groups

DOI10.1515/crll.2003.090zbMath1040.46048arXivmath/0405387OpenAlexW2962877686MaRDI QIDQ4435748

Heath Emerson

Publication date: 18 November 2003

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405387

zbMATH Keywords

\(C^*\)-algebrahyperbolic groupK-theoryBaum-Connes conjecturePoincaré duality

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) Topological methods in group theory (57M07) Exotic index theories on manifolds (58J22) Hyperbolic groups and nonpositively curved groups (20F67) Index theory (19K56)

Related Items (16)

On finitely summable Fredholm modules from Smale spaces ⋮ \(K\)-homological finiteness and hyperbolic groups ⋮ K-theoretic duality for hyperbolic dynamical systems ⋮ Hyperbolic groupoids and duality ⋮ Groups with Spanier-Whitehead duality ⋮ Spanier–Whitehead K-duality for C∗-algebras ⋮ Poincaré duality for Cuntz-Pimsner algebras ⋮ KK-theoretic duality for proper twisted actions ⋮ A Cuntz-Pimsner model for the \(C^\ast \)-algebra of a graph of groups ⋮ A Lefschetz fixed-point formula for certain orbifold C*-algebras ⋮ Limit sets as examples in noncommutative geometry ⋮ D-branes, RR-fields and duality on noncommutative manifolds ⋮ The class of a fibre in noncommutative geometry ⋮ Transversals, duality, and irrational rotation ⋮ \(E\)-theoretic duality for higher rank graph algebras ⋮ \(kk\)-theory for Banach algebras. II: Equivariance and Green-Julg type theorems

Cites Work

• A groupoid approach to C*-algebras
• Hyperbolic metric spaces and the exotic cohomology Novikov conjecture
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• The Baum-Connes conjecture for amenable foliations
• A small simplification in hyperbolic groups
• Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
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