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.
Citation
Matthew Durham. Samuel J Taylor. "Convex cocompactness and stability in mapping class groups." Algebr. Geom. Topol. 15 (5) 2837 - 2857, 2015. https://doi.org/10.2140/agt.2015.15.2839
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