Convex cocompactness and stability in mapping class groups

Durham, Matthew; Taylor, Samuel J

doi:10.2140/agt.2015.15.2839

¹Department of Mathematics, University of Michigan, 3079 East Hall, 530 Church St., Ann Arbor, MI 48109, USA
²Department of Mathematics, Yale University, 10 Hillhouse Ave., New Haven, CT 06520, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2837-2857

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Résumé

We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show that the stable subgroups of mapping class groups are precisely the convex cocompact subgroups. This generalizes a well-known result of Behrstock and is related to questions asked by Farb and Mosher and by Farb.

DOI : 10.2140/agt.2015.15.2839

Classification : 20F65, 51H05, 57M07, 30F60
Keywords: convex cocompact subgroups of mapping class groups, stability, quasiconvexity, hyperbolic groups

Affiliations des auteurs :

Durham, Matthew ¹ ; Taylor, Samuel J ²

¹ Department of Mathematics, University of Michigan, 3079 East Hall, 530 Church St., Ann Arbor, MI 48109, USA
² Department of Mathematics, Yale University, 10 Hillhouse Ave., New Haven, CT 06520, USA

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Durham, Matthew; Taylor, Samuel J. Convex cocompactness and stability in mapping class groups. Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2837-2857. doi: 10.2140/agt.2015.15.2839

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