A congruence subgroup property for symmetric mapping class groups

2024/08/22 by Marco Boggi, Boggi, Marco
Mathematics · #14G32 (Secondary) #57K20 (Primary) 20F65 #FOS: Mathematics #Functional Equations Stability Results #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2408.12486

openalex publication_date 2024/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the congruence subgroup property for the centralizer of a finite subgroup G in the mapping class group of a hyperbolic oriented and connected surface of finite topological type S such that the genus of the quotient surface S/G is at most 2. As an application, we show that torsion elements in the mapping class group of a surface of genus ≤ 2 are conjugacy distinguished.

Related

• Torsion Elements in the Mapping Class Group of a Surface
• The congruence subgroup property for mapping class groups and the residual finiteness of hyperbolic groups
• Generating mapping class group by two torsion elements
• Arithmetic representations of mapping class groups
• Generating the mapping class group by torsion elements of small order