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This article is available for purchase or by subscription. See below.
Abstract
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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.
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Keywords
knot, unknotting number, signature
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Mathematical Subject Classification 2010
Primary: 57M25
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Milestones
Received: 10 July 2018
Revised: 12 July 2019
Accepted: 12 July 2019
Published: 17 March 2020
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