Arithmetic quotients of the mapping class group

Justin Malestein (Hebrew University)

Abstract: In this talk, I will discuss a procedure for obtaining infinitely many “virtual” arithmetic quotients of mapping class groups of closed surfaces, (surjective maps up to finite index). Specifically, for any irreducible rational representation of a finite group of rank less than g, we produce a corresponding virtual arithmetic quotient of the genus g mapping class group. Particular choices of irreducible representations of finite groups yield arithmetic quotients of type Sp(2m), SO(2m, 2m), and SU(m, m) for arbitrarily large m in every genus. Joint with F. Grunewald, M. Larsen, and A. Lubotzky.