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