Unknotting number is not additive under connected sum
Mark Brittenham, Susan Hermiller
Abstract
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.
arXiv comments
Added new figures, and establish several new corollaries to the main theorem. Many small typographical changes
Linked paper: https://arxiv.org/abs/2506.24088 “Unknotting number is not additive under connected sum” (2025 v1) > We give the first examples of a pair of knots K1,K2 in the 3-sphere for which their unknotting numbers satisfy u(K1#K2)<u(K1)+u(K2) . This answers question 1.69(B)…
According to the actual paper (https://arxiv.org/pdf/2506.24088), it has been an open conjecture since at least 1977. The quote: > Unknotting number has long been conjectured to be additive under connected sum; this conjecture is implicit in the work of Wendt, in one of the…
Linked paper: https://arxiv.org/abs/2506.24088 “Unknotting number is not additive under connected sum” (2025 v1) > We give the first examples of a pair of knots K1,K2 in the 3-sphere for which their unknotting numbers satisfy u(K1#K2)<u(K1)+u(K2) . This answers question 1.69(B)…
altairprimeView on HNParent context
According to the actual paper (https://arxiv.org/pdf/2506.24088), it has been an open conjecture since at least 1977. The quote: > Unknotting number has long been conjectured to be additive under connected sum; this conjecture is implicit in the work of Wendt, in one of the…
awanderingmindView on HNParent context