The twisting number of a ribbon knot is bounded below by its doubly slice genus
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910496683196416 |
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| author | Brejevs, Vitalijs Feller, Peter |
| author_facet | Brejevs, Vitalijs Feller, Peter |
| contents | The twisting number of a ribbon knot $K$ is the minimal number of tangle replacements on the symmetry axis of $J \# -J$ for any knot $J$ that is required to produce a symmetric union diagram of $K$. We prove that the twisting number is bounded below by the doubly slice genus and produce examples of ribbon knots with arbitrarily high twisting number, addressing a problem of Tanaka. As an application, we determine hitherto unknown doubly slice genera of some knots with 12 crossings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The twisting number of a ribbon knot is bounded below by its doubly slice genus Brejevs, Vitalijs Feller, Peter Geometric Topology 57K10, 57K30, 57K40 The twisting number of a ribbon knot $K$ is the minimal number of tangle replacements on the symmetry axis of $J \# -J$ for any knot $J$ that is required to produce a symmetric union diagram of $K$. We prove that the twisting number is bounded below by the doubly slice genus and produce examples of ribbon knots with arbitrarily high twisting number, addressing a problem of Tanaka. As an application, we determine hitherto unknown doubly slice genera of some knots with 12 crossings. |
| title | The twisting number of a ribbon knot is bounded below by its doubly slice genus |
| topic | Geometric Topology 57K10, 57K30, 57K40 |
| url | https://arxiv.org/abs/2404.07619 |