Symmetric ribbon numbers of low-complexity knots
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866914623410667520 |
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| author | Akash, Sajid Raihan Corrado, Eric Placke, Bishop Sanketh, Sam Starns, Nick Timothy, Anok Zupan, Alexander |
| author_facet | Akash, Sajid Raihan Corrado, Eric Placke, Bishop Sanketh, Sam Starns, Nick Timothy, Anok Zupan, Alexander |
| contents | Every knot $K \subset S^3$ that admits a symmetric union presentation bounds an immersed ribbon disk in $S^3$, while the converse is an open problem due to Christoph Lamm. The symmetric ribbon number $r_s(K)$ of $K$ is the minimum number of ribbon singularities in any symmetric ribbon disk bounded by $K$. In this paper, we undertake a systematic investigation of symmetric ribbon numbers of knots with at most 12 crossings. Along the way, we exhibit novel lower bounds for $r_s(K)$ arising from knot determinants, Alexander polynomials, Jones polynomials, and Kauffman polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetric ribbon numbers of low-complexity knots Akash, Sajid Raihan Corrado, Eric Placke, Bishop Sanketh, Sam Starns, Nick Timothy, Anok Zupan, Alexander Geometric Topology 57K10, 57K14 Every knot $K \subset S^3$ that admits a symmetric union presentation bounds an immersed ribbon disk in $S^3$, while the converse is an open problem due to Christoph Lamm. The symmetric ribbon number $r_s(K)$ of $K$ is the minimum number of ribbon singularities in any symmetric ribbon disk bounded by $K$. In this paper, we undertake a systematic investigation of symmetric ribbon numbers of knots with at most 12 crossings. Along the way, we exhibit novel lower bounds for $r_s(K)$ arising from knot determinants, Alexander polynomials, Jones polynomials, and Kauffman polynomials. |
| title | Symmetric ribbon numbers of low-complexity knots |
| topic | Geometric Topology 57K10, 57K14 |
| url | https://arxiv.org/abs/2606.02390 |