All finite groups are involved in the mapping class group

Masbaum, Gregor; Reid, Alan W

doi:10.2140/gt.2012.16.1393

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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 $Γ_{g}$ denote the orientation-preserving mapping class group of the genus $g \geq 1$ 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 $Γ_{g}$ .

Keywords

mapping class group, finite quotient, representation, Zariski dense subgroup

Mathematical Subject Classification 2010

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/

Volume 16, issue 3 (2012)