The $p$-colorable subgroup of Thompson's group
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929676088246272 |
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| author | Kodama, Yuya Takano, Akihiro |
| author_facet | Kodama, Yuya Takano, Akihiro |
| contents | Recently, Jones introduced a method of constructing knots and links from elements of Thompson's group $F$ by using its unitary representations. He also defined several subgroups of $F$ as the stabilizer subgroups and some researchers studied them algebraically. One of the subgroups is called the 3-colorable subgroup $\mathcal{F}$, and the authors proved that all knots and links obtained from non-trivial elements of $\mathcal{F}$ are 3-colorable. In this paper, for any odd integer $p$ greater than two, we define the $p$-colorable subgroup of $F$ whose non-trivial elements yield $p$-colorable knots and links and show it is isomorphic to the certain Brown--Thompson group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_10060 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $p$-colorable subgroup of Thompson's group Kodama, Yuya Takano, Akihiro Group Theory Geometric Topology 20F65 (Primary) 57K10 (Secondary) Recently, Jones introduced a method of constructing knots and links from elements of Thompson's group $F$ by using its unitary representations. He also defined several subgroups of $F$ as the stabilizer subgroups and some researchers studied them algebraically. One of the subgroups is called the 3-colorable subgroup $\mathcal{F}$, and the authors proved that all knots and links obtained from non-trivial elements of $\mathcal{F}$ are 3-colorable. In this paper, for any odd integer $p$ greater than two, we define the $p$-colorable subgroup of $F$ whose non-trivial elements yield $p$-colorable knots and links and show it is isomorphic to the certain Brown--Thompson group. |
| title | The $p$-colorable subgroup of Thompson's group |
| topic | Group Theory Geometric Topology 20F65 (Primary) 57K10 (Secondary) |
| url | https://arxiv.org/abs/2302.10060 |