Unknotting number is not additive under connected sum

Published 30 Jun 2025 in math.GT | (2506.24088v1)

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.

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arXiv:2506.24088 [math.GT]: Unknotting number is not additive under connected sum - Mark Brittenham, Susan Hermiller (149 points, 37 comments)

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Unknotting number is not additive under connected sum (12 likes, 0 questions)