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.
Cite this article
Cornelia Druţu Badea, Relatively hyperbolic groups: geometry and quasi-isometric invariance. Comment. Math. Helv. 84 (2009), no. 3, pp. 503–546DOI 10.4171/CMH/171