English

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.

Keywords

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

R2 v1 2026-06-22T15:57:02.478Z