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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Convex cocompact subgroups of mapping class groups

Benson Farb and Lee Mosher

Geometry & Topology 6 (2002) 91–152

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) ΓG G 1, we prove that if ΓG 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 2000
Primary: 20F67, 20F65
Secondary: 57M07, 57S25
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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
Benson Farb
Department of Mathematics
University of Chicago
5734 University Ave
Chicago
Illinois 60637
USA
Lee Mosher
Department of Mathematics and Computer Science
Rutgers University
Newark
New Jersey 07102
USA