On the smallest non-trivial quotients of mapping class groups

Abstract

We prove that the smallest non-trivial quotient of the mapping class group of a connected orientable surface of genus $g\ge 3$ without punctures is Sp${}_{2g}(2)$, thus confirming a conjecture of Zimmermann. In the process, we generalise Korkmaz’s results on $\mathbb{C}$-linear representations of mapping class groups to projective representations over any field.