Unknotting number is not additive under connected sum

Fuente: arXiv
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Main Authors: Brittenham, Mark, Hermiller, Susan
Format: Preprint
Published: 2025
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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