Statistically convex-cocompact actions of groups with contracting elements

2016/12/12 by Wenyuan Yang, Yang, Wenyuan · 7 citations
Computer Science · Mathematics · #20F67 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary 20F65 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1612.03648

openalex publication_date 2016/12/12 · openalex created_date 2017/02/17 · openalex updated_date 2026/07/28

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.

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• Classification of horospherical invariant measures in higher rank
• Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups
• Boundary actions of CAT(0) spaces: topological freeness and applications to C^*-algebras

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