Vol. 305, No. 1, 2020

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Signature invariants related to the unknotting number

Charles Livingston

Vol. 305 (2020), No. 1, 229–250
Abstract

New lower bounds on the unknotting number of a knot are constructed from the classical knot signature function. These bounds can be twice as strong as previously known signature bounds. They can also be stronger than known bounds arising from Heegaard Floer and Khovanov homology. Results include new bounds on the Gordian distance between knots and information about four-dimensional knot invariants. By considering a related nonbalanced signature function, bounds on the unknotting number of slice knots are constructed; these are related to the property of double-sliceness.

Keywords
knot, unknotting number, signature
Mathematical Subject Classification 2010
Primary: 57M25
Milestones
Received: 10 July 2018
Revised: 12 July 2019
Accepted: 12 July 2019
Published: 17 March 2020
Authors
Charles Livingston
Department of Mathematics
Indiana University
Bloomington, IN
United States