Arithmetic representations of mapping class groups
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866908371501711360 |
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| author | Looijenga, Eduard |
| author_facet | Looijenga, Eduard |
| contents | Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the $G$-centralizer in $Sp(H_1(S))$. We give a sufficient condition for its image to be a subgroup of finite index and a weaker condition for this to have no finite nonzero orbit (the Putman-Wieland property). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12791 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Arithmetic representations of mapping class groups Looijenga, Eduard Geometric Topology Algebraic Geometry Group Theory 57K20, 57M12, 11E39 Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the $G$-centralizer in $Sp(H_1(S))$. We give a sufficient condition for its image to be a subgroup of finite index and a weaker condition for this to have no finite nonzero orbit (the Putman-Wieland property). |
| title | Arithmetic representations of mapping class groups |
| topic | Geometric Topology Algebraic Geometry Group Theory 57K20, 57M12, 11E39 |
| url | https://arxiv.org/abs/2108.12791 |