## Geometry & Topology

### All finite groups are involved in the mapping class group

#### Abstract

Let $Γg$ denote the orientation-preserving mapping class group of the genus $g≥1$ 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 $Γg$.

#### Article information

Source
Geom. Topol., Volume 16, Number 3 (2012), 1393-1411.

Dates
Revised: 11 May 2012
Accepted: 5 March 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732440

Digital Object Identifier
doi:10.2140/gt.2012.16.1393

Mathematical Reviews number (MathSciNet)
MR2967055

Zentralblatt MATH identifier
1254.57018

Subjects
Primary: 20F38: Other groups related to topology or analysis
Secondary: 57R56: Topological quantum field theories

#### Citation

Masbaum, Gregor; Reid, Alan W. All finite groups are involved in the mapping class group. Geom. Topol. 16 (2012), no. 3, 1393--1411. doi:10.2140/gt.2012.16.1393. https://projecteuclid.org/euclid.gt/1513732440

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