All finite groups are involved in the mapping class group

Series
Geometry Topology Seminar
Time
Friday, November 8, 2013 - 2:05pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
G. Masbaum РInstitut de Math̩matiques de Jussieu
Organizer
Thang Le
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.)