Statistically Convex-Cocompact Actions of Groups with Contracting Elements
Wen-yuan Yang
Source abstract
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 acting on Teichmüller spaces, 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.
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