Linear representations of the mapping class group of dimension at most $3g-3$

Julian Kaufmann; Nick Salter; Zhong Zhang; Xiyan Zhong

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arXiv · 2507.11365

Linear representations of the mapping class group of dimension at most $3g-3$

Julian Kaufmann·Nick Salter·Zhong Zhang·Xiyan Zhong

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Abstract

We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or $2g+1$ (given as the action on the (co)homology of the surface or its unit tangent bundle) with a trivial representation. As a corollary, any linear system on the moduli space of Riemann surfaces of genus $g$ in this range is of algebro-geometric origin.

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BibTeX RIS

Julian Kaufmann, Nick Salter, Zhong Zhang, Xiyan Zhong. 2025-07-15. Linear representations of the mapping class group of dimension at most $3g-3$. https://arxiv.org/abs/2507.11365

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