Band-unknotting numbers and connected sums of knots

Nakisa Ghanbarian; Stanislav Jabuka

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arXiv · 2512.06299

Band-unknotting numbers and connected sums of knots

Nakisa Ghanbarian·Stanislav Jabuka

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Abstract

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 $K$.

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BibTeX RIS

Nakisa Ghanbarian, Stanislav Jabuka. 2025-12-06. Band-unknotting numbers and connected sums of knots. https://arxiv.org/abs/2512.06299

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