Skein module dimensions of mapping tori of the 2-torus
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914207745703936 |
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| author | Kinnear, Patrick |
| author_facet | Kinnear, Patrick |
| contents | We determine the dimension of the Kauffman bracket skein module at generic $q$ for mapping tori of the 2-torus, generalising the well-known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild homology of the $G$-skein algebra for $G = \mathrm{SL}_N$ or $\mathrm{GL}_N$, which is a direct summand of the whole skein module, and from which the dimensions follow easily in the cases $G = \mathrm{SL}_2$ and $G = \mathrm{GL}_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07332 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Skein module dimensions of mapping tori of the 2-torus Kinnear, Patrick Geometric Topology Quantum Algebra 57K31, 57K16, 57R56 (Primary), 57R22, 16E40 (Secondary) We determine the dimension of the Kauffman bracket skein module at generic $q$ for mapping tori of the 2-torus, generalising the well-known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild homology of the $G$-skein algebra for $G = \mathrm{SL}_N$ or $\mathrm{GL}_N$, which is a direct summand of the whole skein module, and from which the dimensions follow easily in the cases $G = \mathrm{SL}_2$ and $G = \mathrm{GL}_1$. |
| title | Skein module dimensions of mapping tori of the 2-torus |
| topic | Geometric Topology Quantum Algebra 57K31, 57K16, 57R56 (Primary), 57R22, 16E40 (Secondary) |
| url | https://arxiv.org/abs/2304.07332 |