#### Volume 16, issue 3 (2012)

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All finite groups are involved in the mapping class group

### Gregor Masbaum and Alan W Reid

Geometry & Topology 16 (2012) 1393–1411
##### 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 ${\Gamma }_{g}$.

##### Keywords
mapping class group, finite quotient, representation, Zariski dense subgroup
Primary: 20F38
Secondary: 57R56
##### Publication
Received: 22 September 2011
Revised: 11 May 2012
Accepted: 5 March 2012
Published: 24 July 2012
Proposed: Benson Farb
Seconded: Ronald J Stern, Martin R Bridson
##### Authors
 Gregor Masbaum Institut de Mathématiques de Jussieu (UMR 7586 du CNRS) Case 247 4 pl. Jussieu 75252 Cedex 5 Paris France http://www.math.jussieu.fr/~masbaum/ Alan W Reid Department of Mathematics University of Texas 1 Station C1200 Austin TX 78712-0257 USA http://www.ma.utexas.edu/users/areid/