On the Surjecting Class Group of a Surface

Abelian quotients of subgroups of the mapping class group and higher Prym representations

We prove that if a well-known conjecture asserts that the mapping class group of a surface does not virtually surject onto if the genus of the surface is large, then it also holds for all larger genera.We also prove that if there is a counterexample to this conjecture, then there must be a counterexample of a particularly simple form.We prove these results by relating the conjecture to a family of linear representations of the mapping class group that we call the higher prym representations.