Vol. 301, No. 1, 2019

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Unknotting number and Khovanov homology

Akram Alishahi

Vol. 301 (2019), No. 1, 15–29
DOI: 10.2140/pjm.2019.301.15
Abstract

We show that the order of h-torsion homology classes in the Bar-Natan deformation of Khovanov homology with 2-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 |s(K)2|, where s(K) is the Rasmussen s invariant defined by the Bar-Natan spectral sequence.

Keywords
unknotting number, Khovanov homology, Bar-Natan homology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Milestones
Received: 3 June 2018
Revised: 14 September 2018
Accepted: 15 November 2018
Published: 16 September 2019
Authors
Akram Alishahi
Department of Mathematics
Columbia University
New York, NY
United States