Unknotting number is not additive under connected sum
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911152301146112 |
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| author | Brittenham, Mark Hermiller, Susan |
| author_facet | Brittenham, Mark Hermiller, Susan |
| contents | We give the first examples of a pair of knots $K_1$,$K_2$ in the 3-sphere for which their unknotting numbers satisfy $u(K_1\#K_2)<u(K_1)+u(K_2)$ . This answers question 1.69(B) from Kirby's problem list, "Problems in low-dimensional topology", in the negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unknotting number is not additive under connected sum Brittenham, Mark Hermiller, Susan Geometric Topology 57K10, 57K31 We give the first examples of a pair of knots $K_1$,$K_2$ in the 3-sphere for which their unknotting numbers satisfy $u(K_1\#K_2)<u(K_1)+u(K_2)$ . This answers question 1.69(B) from Kirby's problem list, "Problems in low-dimensional topology", in the negative. |
| title | Unknotting number is not additive under connected sum |
| topic | Geometric Topology 57K10, 57K31 |
| url | https://arxiv.org/abs/2506.24088 |