Linear representations of the mapping class group of dimension at most $3g-3$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911740110831616 |
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| author | Kaufmann, Julian Salter, Nick Zhang, Zhong Zhong, Xiyan |
| author_facet | Kaufmann, Julian Salter, Nick Zhang, Zhong Zhong, Xiyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear representations of the mapping class group of dimension at most $3g-3$ Kaufmann, Julian Salter, Nick Zhang, Zhong Zhong, Xiyan Geometric Topology Algebraic Geometry 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. |
| title | Linear representations of the mapping class group of dimension at most $3g-3$ |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2507.11365 |