Biorderability of knot quandles of knots up to eight crossings
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912394924523520 |
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| author | Gupta, Vaishnavi Raundal, Hitesh |
| author_facet | Gupta, Vaishnavi Raundal, Hitesh |
| contents | The paper investigates biorderability of knot quandles of prime knots up to eight crossings. We prove that knot quandles of knots $6_3$, $8_7$, $8_8$, $8_{10}$ and $8_{16}$ can not be biorderable. However, we see that knot quandles of knots $4_1$, $6_1$, $6_2$, $7_6$, $7_7$, $8_1$, $8_2$, $8_3$, $8_4$, $8_5$, $8_6$, $8_9$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$, $8_{18}$, $8_{20}$ and $8_{21}$ could be biorderable. We also give linear orders on the generating set of the knot quandle of a knot (among these knots) that could be extendable to biorders on the quandle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Biorderability of knot quandles of knots up to eight crossings Gupta, Vaishnavi Raundal, Hitesh Geometric Topology The paper investigates biorderability of knot quandles of prime knots up to eight crossings. We prove that knot quandles of knots $6_3$, $8_7$, $8_8$, $8_{10}$ and $8_{16}$ can not be biorderable. However, we see that knot quandles of knots $4_1$, $6_1$, $6_2$, $7_6$, $7_7$, $8_1$, $8_2$, $8_3$, $8_4$, $8_5$, $8_6$, $8_9$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$, $8_{18}$, $8_{20}$ and $8_{21}$ could be biorderable. We also give linear orders on the generating set of the knot quandle of a knot (among these knots) that could be extendable to biorders on the quandle. |
| title | Biorderability of knot quandles of knots up to eight crossings |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2505.19573 |