Relatively hyperbolic groups: geometry and quasi-isometric invariance

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.

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

References in corpus (1)

• Quasi-isometry rigidity of groups

Cited by in corpus (1)

• Lacunary hyperbolic groups