Kauffman bracket skein module of two families of Seifert manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909605328584704 |
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| author | Liang, Minyi Shi, Shangjun Wang, Xiao |
| author_facet | Liang, Minyi Shi, Shangjun Wang, Xiao |
| contents | We compute the Kauffman bracket skein modules of Seifert manifolds $Σ_{0,1}((k_1,1),(k_2,1))$ and $Σ_{0,0}((k_1,1),(k_2,1),(k_3,1))$ by providing presentations of them. From the obtained presentations, we show that the Kauffman bracket skein modules of $Σ_{0,1}((k_1,1),(k_2,1))$ are free with infinitely many generators when $k_1,k_2\ge 1$ and that of $Σ_{0,0}((k_1,1),(k_2,1),(k_3,1))$ are finitely generated when $k_1,k_2,k_3 \ge 2$. We also show that the empty link in either case is not trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kauffman bracket skein module of two families of Seifert manifolds Liang, Minyi Shi, Shangjun Wang, Xiao Geometric Topology 57K31, 57K10 We compute the Kauffman bracket skein modules of Seifert manifolds $Σ_{0,1}((k_1,1),(k_2,1))$ and $Σ_{0,0}((k_1,1),(k_2,1),(k_3,1))$ by providing presentations of them. From the obtained presentations, we show that the Kauffman bracket skein modules of $Σ_{0,1}((k_1,1),(k_2,1))$ are free with infinitely many generators when $k_1,k_2\ge 1$ and that of $Σ_{0,0}((k_1,1),(k_2,1),(k_3,1))$ are finitely generated when $k_1,k_2,k_3 \ge 2$. We also show that the empty link in either case is not trivial. |
| title | Kauffman bracket skein module of two families of Seifert manifolds |
| topic | Geometric Topology 57K31, 57K10 |
| url | https://arxiv.org/abs/2409.09438 |