Pulling back stability with applications to Out($F_n$) and relatively hyperbolic groups
Geometric Topology
2017-09-20 v2 Group Theory
Metric Geometry
Abstract
We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex cocompact subgroups of both mapping class groups and outer automorphism groups of free groups are stable. We also characterize stability in relatively hyperbolic groups whose parabolic subgroups have linear divergence.
Cite
@article{arxiv.1609.06698,
title = {Pulling back stability with applications to Out($F_n$) and relatively hyperbolic groups},
author = {Tarik Aougab and Matthew Gentry Durham and Samuel J. Taylor},
journal= {arXiv preprint arXiv:1609.06698},
year = {2017}
}
Comments
21 pages, 1 figure. Update includes some corrections and revisions. To appear in JLMS