Band-unknotting numbers and connected sums of knots
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908696556077056 |
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| author | Ghanbarian, Nakisa Jabuka, Stanislav |
| author_facet | Ghanbarian, Nakisa Jabuka, Stanislav |
| contents | We study the band-unknotting number $u_{nb}(K)$ of a knot $K$, and how it behaves with respect to connect sums. We show that this sub-additive function is not additive under connected sums, by finding infinitely many examples of knots $K_1, K_2$ with $u_{nb}(K_1\#K_2) < u_{nb}(K_1) + u_{nb}(K_2)$. Even more surprisingly, there are infinitely many examples of knots $K_1, K_2$ such that $u_{nb}(K_1\#K_2) < u_{nb}(K_i)$, $i=1,2$. Our work is motivated by the recent analogous results for the Gordian unknotting number by Brittenham and Hermiller \cite{BrittenhamHermiller}.
We also prove new lower and upper bounds on the topological and smooth non-orientable 4-genus of a knot $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Band-unknotting numbers and connected sums of knots Ghanbarian, Nakisa Jabuka, Stanislav Geometric Topology 57K10, 57K31 We study the band-unknotting number $u_{nb}(K)$ of a knot $K$, and how it behaves with respect to connect sums. We show that this sub-additive function is not additive under connected sums, by finding infinitely many examples of knots $K_1, K_2$ with $u_{nb}(K_1\#K_2) < u_{nb}(K_1) + u_{nb}(K_2)$. Even more surprisingly, there are infinitely many examples of knots $K_1, K_2$ such that $u_{nb}(K_1\#K_2) < u_{nb}(K_i)$, $i=1,2$. Our work is motivated by the recent analogous results for the Gordian unknotting number by Brittenham and Hermiller \cite{BrittenhamHermiller}. We also prove new lower and upper bounds on the topological and smooth non-orientable 4-genus of a knot $K$. |
| title | Band-unknotting numbers and connected sums of knots |
| topic | Geometric Topology 57K10, 57K31 |
| url | https://arxiv.org/abs/2512.06299 |