Convex cocompactness and stability in mapping class groups

Abstract

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-Mosher and Farb.

15 pages, 1 figure

References in corpus (3)

• Hyperbolicity in Teichmüller space
• Knots, sutures and excision
• Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups

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