On closed 3-braids with unknotting number one

Abstract

We prove that if an alternating 3-braid knot has unknotting number one, then there must exist an unknotting crossing in any alternating diagram of it, and we enumerate such knots. The argument combines the obstruction to unknotting number one developed by Ozsváth and Szabó using Heegaard Floer homology, together with one coming from Donaldson's Theorem A.

29 pages, 4 figures

References in corpus (2)

• On the Khovanov and knot Floer homologies of quasi-alternating links
• The slice-ribbon conjecture for 3-stranded pretzel knots

Cited by in corpus (2)

• The rational Witt class and the unknotting number of a knot
• Homologically thin, non-quasi-alternating links