Word hyperbolic extensions of surface groups

2005/05/12 by Ursula Hamenstaedt, Hamenstaedt, Ursula · 3 citations
Computer Science · Mathematics · #20F67 #30F60 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0505244

openalex publication_date 2005/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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