Relatively hyperbolic groups: geometry and quasi-isometric invariance

2006/05/08 by Cornelia Drutu, Drutu, Cornelia · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.math/0605211

34 pages, Latex; added references, corrected typos, pictures included in the Latex file

arxiv created 2006/08/15 · arxiv updated 2009/12/01

Abstract

In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence for every quasi-geodesic triangle of a central left coset of peripheral subgroup.

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• Finite Index Rigidity of Relatively Hyperbolic Groups

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