Algebraic & Geometric Topology

Convex cocompactness and stability in mapping class groups

Matthew Durham and Samuel J Taylor

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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 and Mosher and by Farb.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 5 (2015), 2837-2857.

Dates
Received: 2 July 2014
Revised: 1 January 2015
Accepted: 12 March 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841034

Digital Object Identifier
doi:10.2140/agt.2015.15.2839

Mathematical Reviews number (MathSciNet)
MR3426695

Zentralblatt MATH identifier
1364.20027

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 51H05: General theory
Secondary: 57M07: Topological methods in group theory 30F60: Teichmüller theory [See also 32G15]

Keywords
convex cocompact subgroups of mapping class groups stability quasiconvexity hyperbolic groups

Citation

Durham, Matthew; Taylor, Samuel J. Convex cocompactness and stability in mapping class groups. Algebr. Geom. Topol. 15 (2015), no. 5, 2837--2857. doi:10.2140/agt.2015.15.2839. https://projecteuclid.org/euclid.agt/1510841034


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