All finite groups are involved in the Mapping Class Group

Abstract

Let ${\Gamma }_g$ denote the orientation-preserving Mapping Class Group of the genus $g\ge 1$ closed orientable surface. In this paper we show that for fixed $g$, every finite group occurs as a quotient of a finite index subgroup of ${\Gamma }_g$.

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

References in corpus (1)

• Quantum invariants of random 3-manifolds

Cited by in corpus (3)

• Vastness properties of automorphism groups of RAAGs
• Profinite completions of Burnside-type quotients of surface groups
• On finite index subgroups of the mapping class group of a nonorientable surface