arXiv:1404.4803 Abstract | arXiv Analytics

arXiv:1404.4803 [math.GT]Abstract References Reviews Resources

Convex cocompactness and stability in mapping class groups

Published 2014-04-18Version 1

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.

Comments: 15 pages, 1 figure

Categories: math.GT, math.GR

Keywords: mapping class groups, convex cocompactness, finitely generated groups, convex cocompact subgroups, stability agrees

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