All finite groups are involved in the mapping class group

Geometry Topology Seminar
Friday, November 8, 2013 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Institut de Mathématiques de Jussieu
Let g be a positive integer and let Gamma_g be the mapping class group of the genus g closed orientable surface. We show that every finite group is involved in Gamma_g. (Here a group G is said to be involved in a group Gamma if G is isomorphic to a quotient of a subgroup of Gamma of finite index.) This answers a question asked by U. Hamenstadt. The proof uses quantum representations of mapping class groups. (Joint work with A. Reid.)