Statistically Convex-Cocompact Actions of Groups with Contracting Elements. (5th February 2018)

• Record Type: Journal Article
• Authors: Yang, Wen-yuan
• Is Part Of: International mathematics research notices. Volume 2019:Number 23(2019)
• Page Start: 7259
• Page End: 7323
• Publication Date: 2018-02-05
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rny001
• Languages: English
• ISSNs: 1073-7928

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.