A remark on the counterexample to the unknotting number conjecture
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916850098503680 |
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| author | Wang, Chao Zhang, Yimu |
| author_facet | Wang, Chao Zhang, Yimu |
| contents | By using Snappy, M. Brittenham and S. Hermiller discovered a very surprising example that $u(7_1\#\overline{7_1})\leq 5<6=u(7_1)+u(\overline{7_1})$, where $7_1$ is the $(2,7)$-torus knot and $\overline{7_1}$ is its mirror image. Based on their work, we give a direct verification of this fact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on the counterexample to the unknotting number conjecture Wang, Chao Zhang, Yimu Geometric Topology 57K10 By using Snappy, M. Brittenham and S. Hermiller discovered a very surprising example that $u(7_1\#\overline{7_1})\leq 5<6=u(7_1)+u(\overline{7_1})$, where $7_1$ is the $(2,7)$-torus knot and $\overline{7_1}$ is its mirror image. Based on their work, we give a direct verification of this fact. |
| title | A remark on the counterexample to the unknotting number conjecture |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2507.14265 |