Relatively hyperbolic groups: geometry and quasi-isometric invariance

Cornelia Drutu

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Relatively hyperbolic groups: geometry and quasi-isometric invariance

Cornelia Drutu

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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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Cornelia Drutu. 2006-08-15. Relatively hyperbolic groups: geometry and quasi-isometric invariance. https://arxiv.org/abs/math/0605211

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