On the smallest non-trivial quotients of mapping class groups (Q784891)

Summary: We prove that the smallest non-trivial quotient of the mapping class group of a connected orientable surface of genus \(g \geq 3\) without punctures is \(\text{Sp}_{2g}(2)\), 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.