On Thompson knot theory and conjugacy classes of Thompson's group $F$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912305743134720 |
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| author | Bao, Yuanyuan Sheng, Xiaobing |
| author_facet | Bao, Yuanyuan Sheng, Xiaobing |
| contents | Jones introduced a method to produce unoriented links from elements of the Thompson's group $F$, and proved that any link can be produced by this construction. In this paper, we attempt to investigate the relations between conjugacy classes of the group $F$ and the links being constructed. For each unoriented link $L$, we find a sequence of elements of $F$ from distinct conjugacy classes which yield $L$ via Jones's construction. We also show that a sequence of $2$-bridge links can be constructed from elements in the conjugacy class of $x_0$ (resp. $x_1$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_01714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Thompson knot theory and conjugacy classes of Thompson's group $F$ Bao, Yuanyuan Sheng, Xiaobing Geometric Topology Primary 57K10, Secondary 20F65 Jones introduced a method to produce unoriented links from elements of the Thompson's group $F$, and proved that any link can be produced by this construction. In this paper, we attempt to investigate the relations between conjugacy classes of the group $F$ and the links being constructed. For each unoriented link $L$, we find a sequence of elements of $F$ from distinct conjugacy classes which yield $L$ via Jones's construction. We also show that a sequence of $2$-bridge links can be constructed from elements in the conjugacy class of $x_0$ (resp. $x_1$). |
| title | On Thompson knot theory and conjugacy classes of Thompson's group $F$ |
| topic | Geometric Topology Primary 57K10, Secondary 20F65 |
| url | https://arxiv.org/abs/2504.01714 |