The ${\rm SL}(2,\mathbb{C})$-character variety of an arborescent knot
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913251104653312 |
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| author | Chen, Haimiao |
| author_facet | Chen, Haimiao |
| contents | We clarify steps for determining the ${\rm SL}(2,\mathbb{C})$-character variety of any arborescent knot.
Interestingly, we show that the `excellent parts' of arborescent knots $K_1,K_2$ are isomorphic if $K_1$ can be related to $K_2$ through certain moves on projection diagrams.
Furthermore, we give a sufficient condition in terms of diagram for the existence of components of dimension larger than $1$. A generalization to arborescent links is sketched. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10345 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The ${\rm SL}(2,\mathbb{C})$-character variety of an arborescent knot Chen, Haimiao Geometric Topology 57K10, 57K31 We clarify steps for determining the ${\rm SL}(2,\mathbb{C})$-character variety of any arborescent knot. Interestingly, we show that the `excellent parts' of arborescent knots $K_1,K_2$ are isomorphic if $K_1$ can be related to $K_2$ through certain moves on projection diagrams. Furthermore, we give a sufficient condition in terms of diagram for the existence of components of dimension larger than $1$. A generalization to arborescent links is sketched. |
| title | The ${\rm SL}(2,\mathbb{C})$-character variety of an arborescent knot |
| topic | Geometric Topology 57K10, 57K31 |
| url | https://arxiv.org/abs/2304.10345 |