A refinement of Khovanov homology

Andrew Lobb; Liam Watson

doi:10.2140/gt.2021.25.1861

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2021 A refinement of Khovanov homology

Andrew Lobb, Liam Watson

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.

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Andrew Lobb. Liam Watson. "A refinement of Khovanov homology." Geom. Topol. 25 (4) 1861 - 1917, 2021. https://doi.org/10.2140/gt.2021.25.1861

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Received: 16 September 2019; Revised: 20 January 2020; Accepted: 29 February 2020; Published: 2021

First available in Project Euclid: 12 October 2021

Digital Object Identifier: 10.2140/gt.2021.25.1861

Subjects:

Primary: 57M25 , 57M27 , 57M60

Keywords: Khovanov , knot theory , mutant , strongly invertible

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