Unknotting number is not additive under connected sum

Mark Brittenham; Susan Hermiller

paper

Unknotting number is not additive under connected sum

arXiv:2506.24088

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.

Added new figures, and establish several new corollaries to the main theorem. Many small typographical changes