Word hyperbolic extensions of surface groups

Details Word hyperbolic extensions of surface groups Word hyperbolic extensions of surface groups

2005-05-12

arxiv.org/abs/math/0505244v2

Mathematics

Geometric Topology

Writing improved, references corrected

Scientific paper

Let S be a closed surface of genus at least 2. We show that a finitely
generated group G which is an extension of the fundamental group H of S is word
hyperbolic if and only the orbit map of the quotient group G/H on the complex
of curves is a quasi-isometric embedding.This in turn is equivalent to G/H
being convex cocompact in the sense of Farb and Mosher.

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