Relatively hyperbolic groups: geometry and quasi-isometric invariance

Details Relatively hyperbolic groups: geometry and quasi-isometric invariance Relatively hyperbolic groups: geometry and quasi-isometric invariance

2006-05-08

arxiv.org/abs/math/0605211v4

Mathematics

Group Theory

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

Scientific paper

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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