Geometry & Topology 6 (2002) 91–152

DOI: 10.2140/gt.2002.6.91

arXiv: math.GR/0106190

Abstract

We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmüller space. Given a subgroup G of MCG defining an extension 1→π₁(S)→Γ_G→G→1, we prove that if Γ_G is a word hyperbolic group then G is a convex cocompact subgroup of MCG. When G is free and convex cocompact, it is called a Schottky subgroup.

Keywords

mapping class group, Schottky subgroup, cocompact subgroup, convexity, pseudo-Anosov

Mathematical Subject Classification

Primary: 20F65, 20F67

Secondary: 57M07, 57S25

References

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Publication

Received: 20 October 2001
Accepted: 20 February 2002
Published: 14 March 2002
Proposed: Walter Neumann
Seconded: Shigeyuki Morita, Robion Kirby

Authors