English

All finite groups are involved in the Mapping Class Group

Geometric Topology 2014-11-11 v4

Abstract

Let Γg\Gamma_g denote the orientation-preserving Mapping Class Group of the genus g1g\geq 1 closed orientable surface. In this paper we show that for fixed gg, every finite group occurs as a quotient of a finite index subgroup of Γg\Gamma_g.

Keywords

Cite

@article{arxiv.1106.4261,
  title  = {All finite groups are involved in the Mapping Class Group},
  author = {Gregor Masbaum and Alan W. Reid},
  journal= {arXiv preprint arXiv:1106.4261},
  year   = {2014}
}

Comments

This is the final version submitted to Geometry & Topology, and is almost identical with the published paper

R2 v1 2026-06-21T18:25:36.557Z