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 at least 3 without punctures is ${\mathrm{Sp}}_{2g}(2)$, 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.

18 pages, 2 figures; v.2: Section 2 (on projective representations of mapping class groups) completely rewritten; v.3: Final version, to appear in Groups Geom. Dyn

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