A Topological Characterisation of Hyperbolic Groups
نویسنده
چکیده
The notion of a hyperbolic group was introduced by Gromov [Gr]. Associated to any hyperbolic group, Γ, is its boundary, ∂Γ. This is a metrisable compactum on which Γ acts by homeomorphism. If Γ is non-elementary (i.e. not finite or virtually cyclic), then ∂Γ is perfect. The induced action of Γ on the space of distinct triples of ∂Γ is properly discontinuous and cocompact. The main result of this paper is that this topological property characterises hyperbolic groups. More precisely:
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تاریخ انتشار 1998