All finite groups are involved in the mapping class group

Masbaum, Gregor¹ ; Reid, Alan W²

¹ Institut de Mathématiques de Jussieu (UMR 7586 du CNRS), Case 247, 4 pl. Jussieu, 75252 Cedex 5 Paris, France
² Department of Mathematics, University of Texas, 1 Station C1200, Austin TX 78712-0257, USA

Geometry & topology, Tome 16 (2012) no. 3, pp. 1393-1411.

Résumé

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 ${\Gamma }_g$.

Détail

DOI : 10.2140/gt.2012.16.1393

Classification : 20F38, 57R56
Keywords: mapping class group, finite quotient, representation, Zariski dense subgroup

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