Noncommutative Poincare duality for boundary actions of hyperbolic groups
By Heath Emerson. 2003
57 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/72b7a8d7e4b55c379bae40cf55a79d8c77173e96
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In Geometry and Topology
- Volodymyr V. Nekrashevych
- Enrique Pardo
- R. Exel
- Rostislav I. Grigorchuk
- Yaroslav Vorobets
- Mariya Vorobets
- M. Bonk
- Daniel Meyer
In Mathematical Physics
- Volodymyr V. Nekrashevych
- Enrique Pardo
- R. Exel
- Rostislav I. Grigorchuk
- Yaroslav Vorobets
- Mariya Vorobets
- Daniel Meyer
- M. Bonk
Citations in the corpus
- C*-algebras and self-similar groups (2009, background): “Emerson showed non-commutative Poincaré duality for the cross-product algebras of the action of a Gromov hyperbolic group on its boundary in [17].”