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A refinement of Khovanov homology

Andrew Lobb and Liam Watson

Geometry & Topology 25 (2021) 1861–1917
Abstract

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.

Keywords
Khovanov, mutant, strongly invertible, knot theory
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57M60
References
Publication
Received: 16 September 2019
Revised: 20 January 2020
Accepted: 29 February 2020
Published: 12 July 2021
Proposed: Ciprian Manolescu
Seconded: Haynes R Miller, András I Stipsicz
Authors
Andrew Lobb
Department of Mathematical Sciences
Durham University
Durham
United Kingdom
http://www.maths.dur.ac.uk/users/andrew.lobb/
Liam Watson
Mathematics Department
University of British Columbia
Vancouver, BC
Canada
http://www.math.ubc.ca/~liam