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Groups, Geometry, and Dynamics

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Volume 14, Issue 2, 2020, pp. 489–512
DOI: 10.4171/GGD/552

Published online: 2020-06-22

On the smallest non-trivial quotients of mapping class groups

Dawid Kielak[1] and Emilio Pierro[2]

(1) Universität Bielefeld, Germany
(2) Universität Bielefeld, Germany

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 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.

Keywords: Mapping class groups, finite quotients, projective representations

Kielak Dawid, Pierro Emilio: On the smallest non-trivial quotients of mapping class groups. Groups Geom. Dyn. 14 (2020), 489-512. doi: 10.4171/GGD/552