JournalscmhVol. 84, No. 3pp. 503–546

Relatively hyperbolic groups: geometry and quasi-isometric invariance

  • Cornelia Druţu Badea

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

Cite this article

Cornelia Druţu Badea, Relatively hyperbolic groups: geometry and quasi-isometric invariance. Comment. Math. Helv. 84 (2009), no. 3, pp. 503–546

DOI 10.4171/CMH/171