On the knot quandle of the twist-spun trefoil
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866911134861230080 |
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| author | Inoue, Ayumu |
| author_facet | Inoue, Ayumu |
| contents | We show that the knot quandle of the $3$-, $4$-, or $5$-twist-spun trefoil is isomorphic to a quandle related to the $16$-, $24$-, or $600$-cell respectively. We further show that the cardinality of the knot quandle of the $m$-twist-spun trefoil is finite if and only if $1 \leq m \leq 5$. This phenomenon is attributable to the fact that the regular tessellation $\{ 3, m \}$, in the sense of the Schläfli symbol, consists of infinite triangles if $m$ is greater than or equal to 6. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_06276 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the knot quandle of the twist-spun trefoil Inoue, Ayumu Geometric Topology 57Q45, 52B15 We show that the knot quandle of the $3$-, $4$-, or $5$-twist-spun trefoil is isomorphic to a quandle related to the $16$-, $24$-, or $600$-cell respectively. We further show that the cardinality of the knot quandle of the $m$-twist-spun trefoil is finite if and only if $1 \leq m \leq 5$. This phenomenon is attributable to the fact that the regular tessellation $\{ 3, m \}$, in the sense of the Schläfli symbol, consists of infinite triangles if $m$ is greater than or equal to 6. |
| title | On the knot quandle of the twist-spun trefoil |
| topic | Geometric Topology 57Q45, 52B15 |
| url | https://arxiv.org/abs/1808.06276 |