JournalscmhVol. 84 , No. 3DOI 10.4171/cmh/171

Relatively hyperbolic groups: geometry and quasi-isometric invariance

  • Cornelia Druţu Badea

    Oxford University, United Kingdom
Relatively hyperbolic groups: geometry and quasi-isometric invariance cover

Abstract

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