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A refinement of Khovanov homology

Andrew Lobb and Liam Watson

Geometry & Topology 25 (2021) 1861–1917

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.

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Khovanov, mutant, strongly invertible, knot theory
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57M60
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
Andrew Lobb
Department of Mathematical Sciences
Durham University
United Kingdom
Liam Watson
Mathematics Department
University of British Columbia
Vancouver, BC