Unknotting number is not additive under connected sum — mentioned by awanderingmind

Thu, 04 Sep 2025 06:18:53 GMT

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 first systematic studies of unknotting number [37]. It is unclear when and where this was first explicitly stated; most references to it call it an ‘old conjecture’. It can be found in the problem list of Gordon [13] from 1977 and in Kirby’s list [16]. 'Additive' here means that if u(K1) is defined as the unknotting number…

Paper and discussion history. A mention is not an endorsement.

Unknotting number is not additive under connected sum — mentioned by altairprime

Tue, 02 Sep 2025 15:08:46 GMT

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) from Kirby's problem list, "Problems in low-dimensional topology", in the negative.

Paper and discussion history. A mention is not an endorsement.

Unknotting number is not additive under connected sum · HackerPapers discussions

Unknotting number is not additive under connected sum — mentioned by awanderingmind

Unknotting number is not additive under connected sum — mentioned by altairprime