Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661267 | Topology and its Applications | 2006 | 7 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Geometry and Topology