Statistically convex-cocompact actions of groups with contracting elements
Abstract
This paper presents a study of the asymptotic geometry of groups with contracting elements, with emphasis on a subclass of statistically convex-cocompact (SCC) actions. The class of SCC actions includes relatively hyperbolic groups, CAT(0) groups with rank-1 elements and mapping class groups, among others. We exploit an extension lemma to prove that a group with SCC actions contains large free sub-semigroups, has purely exponential growth and contains a class of barrier-free sets with a growth-tight property. Our study produces new results and recovers existing ones for many interesting groups through a unified and elementary approach.
Cite
@article{arxiv.1612.03648,
title = {Statistically convex-cocompact actions of groups with contracting elements},
author = {Wenyuan Yang},
journal= {arXiv preprint arXiv:1612.03648},
year = {2017}
}
Comments
Version 4. 37 pages, 3 figures. Sections 6-8 in previous version moved to arXiv:1707.06006 as independent paper. A new section "Constructing SCC actions" is added