Convex cocompactness and stability in mapping class groups
Geometric Topology
2015-11-25 v1 Group Theory
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-Mosher and Farb.
Cite
@article{arxiv.1404.4803,
title = {Convex cocompactness and stability in mapping class groups},
author = {Matthew Gentry Durham and Samuel J. Taylor},
journal= {arXiv preprint arXiv:1404.4803},
year = {2015}
}
Comments
15 pages, 1 figure