Unknotting with a single twist

Samantha Allen; Charles Livingston

doi:10.4171/lem/66-3/4-10

JournalslemVol. 66, No. 3/4pp. 541–589

Unknotting with a single twist

Samantha Allen
Dartmouth College, Hanover, USA
Charles Livingston
Indiana University, Bloomington, USA

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Abstract

Given a knot $K \subset S^{3}$ , is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstructions to unknotting using a twist of a specified linking number. The obstructions we describe are built using classical knot invariants, Casson–Gordon invariants, and Heegaard Floer theory.

Cite this article

Samantha Allen, Charles Livingston, Unknotting with a single twist. Enseign. Math. 66 (2020), no. 3/4, pp. 541–589

DOI 10.4171/LEM/66-3/4-10