Boundary amenability of relatively hyperbolic groups
By Nathanial P. Brown Narutaka Ozawa. 2005
83 citations recorded by the source corpus.
Abstract Let K be a fine hyperbolic graph and Γ be a group acting on K with finite quotient. We prove that Γ is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups are exact. We prove this by showing that the group Γ acts amenably on a compact topological space. We include some applications to the theories of group von Neumann algebras and of measurable orbit equivalence relations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/29fd663d4cbc6ac18837a8a7fb9646e28423068f
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In Geometry and Topology
- E. Guentner
- Nathanial P. Brown Narutaka Ozawa
- Marius Dadarlat
- Rufus Willett
- Sorin Popa
- Martin Finn-Sell
- Guoliang Yu
- S. Vaes
In Mathematical Physics
- Nathanial P. Brown Narutaka Ozawa
- E. Guentner
- Marius Dadarlat
- Rufus Willett
- Gilles Pisier
- Sorin Popa
- W. Winter
- Adrian Ioana
Citations in the corpus
- A Kurosh-type theorem for type II1 factors (2004, background): “The class S contains all word hyperbolic groups (and more generally groups which are hyperbolic relative to a family of amenable subgroups) [HG][Oz3][Sk].”
- Uniform embeddability of relatively hyperbolic groups (2005, methodology): “There are two analogous results in the literature: Osin proved an analogous statement for finite asymptotic dimension [12] and Ozawa proved an analogous statement for exactness [14].”