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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

DOI: 10.2140/gt.2012.16.1393
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.

Keywords

mapping class group, finite quotient, representation, Zariski dense subgroup
Mathematical Subject Classification

Primary: 20F38

Secondary: 57R56
References
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/