Vol. 301, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1  2
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
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Unknotting number and Khovanov homology

Akram Alishahi

Vol. 301 (2019), No. 1, 15–29
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