The bridge index and the braid index for twist positive knots
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909730346106880 |
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| author | Himeno, Keisuke |
| author_facet | Himeno, Keisuke |
| contents | In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Morton, we prove that the bridge index and the braid index coincide for all twist positive knots, using the knot Floer torsion order. Here, a twist positive knot is a knot that admits a positive braid representative containing at least one full twist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The bridge index and the braid index for twist positive knots Himeno, Keisuke Geometric Topology 57K10, 57K18 In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Morton, we prove that the bridge index and the braid index coincide for all twist positive knots, using the knot Floer torsion order. Here, a twist positive knot is a knot that admits a positive braid representative containing at least one full twist. |
| title | The bridge index and the braid index for twist positive knots |
| topic | Geometric Topology 57K10, 57K18 |
| url | https://arxiv.org/abs/2507.23252 |