Computation of the knot symmetric quandle and its application to the plat index of surface-links
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929316102668288 |
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| author | Yasuda, Jumpei |
| author_facet | Yasuda, Jumpei |
| contents | A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link $F$ is a pair of a quandle and a good involution determined from $F$. In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers $g \geq 0$ and $m \geq 2$, there exists infinitely many distinct surface-knots of genus $g$ whose plat indices are $m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14488 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computation of the knot symmetric quandle and its application to the plat index of surface-links Yasuda, Jumpei Geometric Topology 57K45 (Primary) 57K10 (Secondary) A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link $F$ is a pair of a quandle and a good involution determined from $F$. In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers $g \geq 0$ and $m \geq 2$, there exists infinitely many distinct surface-knots of genus $g$ whose plat indices are $m$. |
| title | Computation of the knot symmetric quandle and its application to the plat index of surface-links |
| topic | Geometric Topology 57K45 (Primary) 57K10 (Secondary) |
| url | https://arxiv.org/abs/2308.14488 |