R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916564234665984 |
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| author | Sato, Mai |
| author_facet | Sato, Mai |
| contents | We introduce a new equivalence relation, named R-equivalence relation, on the set of colorings of an oriented knot diagram by a quandle. We determine the R-equivalence classes of colorings of a diagram of a torus knot by a quandle, called $\mathrm{Rot} \mathbb{E}^{2}$, under a certain condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots Sato, Mai Geometric Topology 57K12, 57K10 We introduce a new equivalence relation, named R-equivalence relation, on the set of colorings of an oriented knot diagram by a quandle. We determine the R-equivalence classes of colorings of a diagram of a torus knot by a quandle, called $\mathrm{Rot} \mathbb{E}^{2}$, under a certain condition. |
| title | R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots |
| topic | Geometric Topology 57K12, 57K10 |
| url | https://arxiv.org/abs/2501.07031 |