Vol. 301, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
Unknotting number and Khovanov homology

Akram Alishahi

Vol. 301 (2019), No. 1, 15–29

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.

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