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Convex cocompactness
and stability in mapping class groups
Matthew Gentry Durham and Samuel J Taylor |
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Algebraic & Geometric Topology 15 (2015) 2837–2857
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Abstract |
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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. |
Keywords
convex cocompact subgroups of mapping class groups,
stability, quasiconvexity, hyperbolic groups
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Mathematical Subject Classification 2010
Primary: 20F65, 51H05
Secondary: 57M07, 30F60
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References |
Publication
Received: 2 July 2014
Revised: 1 January 2015
Accepted: 12 March 2015
Published: 10 December 2015
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Authors |
| Matthew Gentry Durham | |
| Department of Mathematics University of Michigan 3079 East Hall 530 Church St. Ann Arbor, MI 48109 USA |
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| http://www-personal.umich.edu/~durhamma/ | |
| Samuel J Taylor | |
| Department of Mathematics Yale University 10 Hillhouse Ave. New Haven, CT 06520 USA |
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| http://users.math.yale.edu/users/taylor/ | |
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