Non-braid positive hyperbolic $L$-space knots
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917443709960192 |
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| author | Himeno, Keisuke |
| author_facet | Himeno, Keisuke |
| contents | An $L$-space knot is a knot that admits a positive Dehn surgery yielding an $L$-space. Many known hyperbolic $L$-space knots are braid positive, meaning they can be represented as the closure of a positive braid. Recently, Baker and Kegel showed that the hyperbolic $L$-space knot $o9\_30634$ from Dunfield's census is not braid positive, and they constructed infinitely many candidates for hyperbolic $L$-space knots that may not be braid positive. However, it remains unproven whether their examples are genuinely non-braid positive. In this paper, we construct infinitely many hyperbolic $L$-space knots that are not braid positive, and our examples are distinct from those considered by Baker and Kegel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-braid positive hyperbolic $L$-space knots Himeno, Keisuke Geometric Topology 57K10, 57K18 An $L$-space knot is a knot that admits a positive Dehn surgery yielding an $L$-space. Many known hyperbolic $L$-space knots are braid positive, meaning they can be represented as the closure of a positive braid. Recently, Baker and Kegel showed that the hyperbolic $L$-space knot $o9\_30634$ from Dunfield's census is not braid positive, and they constructed infinitely many candidates for hyperbolic $L$-space knots that may not be braid positive. However, it remains unproven whether their examples are genuinely non-braid positive. In this paper, we construct infinitely many hyperbolic $L$-space knots that are not braid positive, and our examples are distinct from those considered by Baker and Kegel. |
| title | Non-braid positive hyperbolic $L$-space knots |
| topic | Geometric Topology 57K10, 57K18 |
| url | https://arxiv.org/abs/2506.22934 |