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Convex cocompactness and stability in mapping class groups
Durham, MG Taylor, SJ
Durham, MG
Taylor, SJ
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Journal Article
Date
2015-11-12
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10.2140/agt.2015.15.2839
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© 2015, Mathematical Sciences Publishers. All rights reserved. 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.
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Mathematical Sciences Publishers
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Algebraic and Geometric Topology
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