A congruence subgroup property for symmetric mapping class groups

Marco Boggi

A congruence subgroup property for symmetric mapping class groups

Geometric Topology 2026-01-15 v2 Group Theory

Authors: Marco Boggi

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 $\leq 2$ are conjugacy distinguished.

Keywords

mapping class groups of surfaces mapping class groups conjugacy classes in groups

Cite

@article{arxiv.2408.12486,
  title  = {A congruence subgroup property for symmetric mapping class groups},
  author = {Marco Boggi},
  journal= {arXiv preprint arXiv:2408.12486},
  year   = {2026}
}

Comments

8 pages

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