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This article is available for purchase or by subscription. See below.
Abstract
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We show that the order of
-torsion
homology classes in the Bar-Natan deformation of Khovanov homology with
-coefficients
is a lower bound for the unknotting number. This is not a bound for the slice genus,
unlike most lower bounds for the unknotting number, and only vanishes for the
unknot. We give examples of knots for which this is a better lower bound than
, where
is the
Rasmussen
invariant defined by the Bar-Natan spectral sequence.
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Keywords
unknotting number, Khovanov homology, Bar-Natan homology
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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Milestones
Received: 3 June 2018
Revised: 14 September 2018
Accepted: 15 November 2018
Published: 16 September 2019
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