Dynamics of subgroups of mapping class groups

2023/11/07 by Ilya Gekhtman, Biao Ma, Gekhtman, Ilya +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2311.03779

openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \rmMod(S) be the mapping class group of a closed orientable surface S of genus g ≥ 2. Let G be a non-elementary subgroup of \rmMod(S) so that the associated Bowen-Margulis measure is finite. In this paper, we give an asymptotic growth formula for G with respect to the Teichmüller metric.

Related

• Uniform uniform exponential growth of subgroups of the mapping class group
• Geometric survey of subgroups of mapping class groups
• Estimating the distances between hyperbolic structures in the moduli space
• Boundary representations of mapping class groups
• Reduction theory for mapping class groups and applications to moduli spaces