Unknotting number and connected sums: The knots $4_1$ and $5_1$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910001173364736 |
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| author | Brittenham, Mark Hermiller, Susan |
| author_facet | Brittenham, Mark Hermiller, Susan |
| contents | We show that the knots $K\in\{4_1,5_1\}$ can be paired with a corresponding knot $K^\prime$ such that $u(K\#K^\prime)<u(K)+u(K^\prime)$. As a consequence unknotting number fails to be additive for these knots. We also provide a candidate knot $K^\prime$ for the knot $3_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18757 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unknotting number and connected sums: The knots $4_1$ and $5_1$ Brittenham, Mark Hermiller, Susan Geometric Topology 57K10, 57K31 We show that the knots $K\in\{4_1,5_1\}$ can be paired with a corresponding knot $K^\prime$ such that $u(K\#K^\prime)<u(K)+u(K^\prime)$. As a consequence unknotting number fails to be additive for these knots. We also provide a candidate knot $K^\prime$ for the knot $3_1$. |
| title | Unknotting number and connected sums: The knots $4_1$ and $5_1$ |
| topic | Geometric Topology 57K10, 57K31 |
| url | https://arxiv.org/abs/2601.18757 |