Convex cocompact subgroups of mapping class groups

Farb, Benson¹ ; Mosher, Lee²

¹ Department of Mathematics, University of Chicago, 5734 University Ave, Chicago, Illinois 60637, USA
² Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102, USA

Geometry & topology, Tome 6 (2002) no. 1, pp. 91-152.

Résumé

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 $1\to {\pi }_1\left(S\right)\to {\Gamma }_G\to G\to 1$, we prove that if ${\Gamma }_G$ 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.

Détail

DOI : 10.2140/gt.2002.6.91

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

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