Higher Prym Representations of the Mapping Class Group

Geometry Topology Student Seminar
Wednesday, February 20, 2013 - 11:05
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
A conjecture of Ivanov asserts that finite index subgroups of the mapping class group of higher genus surfaces have trivial rational homology.  Putman and Wieland use what they call higher Prym representations, which are extensions of the representation induced by the action of the mapping class group on homology, to better understand the conjecture.  In particular, they prove that if Ivanov's conjecture is true for some genus g surface, it is true for all higher genus surfaces.  On the other hand, they also prove that if there is a counterexample to Ivanov's conjecture, it is of a specific form.