Action of subgroups of the mapping class group on Heisenberg homologies
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912585064906752 |
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| author | Blanchet, Christian Palmer, Martin Shaukat, Awais |
| author_facet | Blanchet, Christian Palmer, Martin Shaukat, Awais |
| contents | In previous work we constructed twisted representations of mapping class groups of surfaces, depending on a choice of representation $V$ of the Heisenberg group $\mathcal{H}$. For certain $V$ we were able to untwist these mapping class group representations. Here, we study the restrictions of our twisted representations to different subgroups of the mapping class group. In particular, we prove that these representations may be untwisted on the Torelli group for any given representation $V$ of $\mathcal{H}$. When $V$ is the Schrödinger representation, we also construct untwisted representations of subgroups defined as kernels of crossed homomorphisms studied by Earle and Morita. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Action of subgroups of the mapping class group on Heisenberg homologies Blanchet, Christian Palmer, Martin Shaukat, Awais Geometric Topology Algebraic Topology 57K20, 55R80, 55N25, 20C12, 19C09 In previous work we constructed twisted representations of mapping class groups of surfaces, depending on a choice of representation $V$ of the Heisenberg group $\mathcal{H}$. For certain $V$ we were able to untwist these mapping class group representations. Here, we study the restrictions of our twisted representations to different subgroups of the mapping class group. In particular, we prove that these representations may be untwisted on the Torelli group for any given representation $V$ of $\mathcal{H}$. When $V$ is the Schrödinger representation, we also construct untwisted representations of subgroups defined as kernels of crossed homomorphisms studied by Earle and Morita. |
| title | Action of subgroups of the mapping class group on Heisenberg homologies |
| topic | Geometric Topology Algebraic Topology 57K20, 55R80, 55N25, 20C12, 19C09 |
| url | https://arxiv.org/abs/2306.08614 |