A topological characterisation of hyperbolic groups

Bowditch, Brian

doi:10.1090/S0894-0347-98-00264-1

A topological characterisation of hyperbolic groups
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by Brian H. Bowditch

J. Amer. Math. Soc. 11 (1998), 643-667

DOI: https://doi.org/10.1090/S0894-0347-98-00264-1

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Abstract:

We characterise word hyperbolic groups as those groups which act properly discontinuously and cocompactly on the space of distinct triples of a compact metrisable space. This is, in turn, equivalent to a convergence group for which every point of the space is a conical limit point.

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