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2020 On spectral sequences from Khovanov homology
Andrew Lobb, Raphael Zentner
Algebr. Geom. Topol. 20(2): 531-564 (2020). DOI: 10.2140/agt.2020.20.531

Abstract

There are a number of homological knot invariants, each satisfying an unoriented skein exact sequence, which can be realised as the limit page of a spectral sequence starting at a version of the Khovanov chain complex. Compositions of elementary 1–handle movie moves induce a morphism of spectral sequences. These morphisms remain unexploited in the literature, perhaps because there is still an open question concerning the naturality of maps induced by general movies.

Here we focus on the spectral sequence due to Kronheimer and Mrowka from Khovanov homology to instanton knot Floer homology, and on that due to Ozsváth and Szabó to the Heegaard Floer homology of the branched double cover. For example, we use the 1–handle morphisms to give new information about the filtrations on the instanton knot Floer homology of the (4,5)–torus knot, determining these up to an ambiguity in a pair of degrees; to determine the Ozsváth–Szabó spectral sequence for an infinite class of prime knots; and to show that higher differentials of both the Kronheimer–Mrowka and the Ozsváth–Szabó spectral sequences necessarily lower the delta grading for all pretzel knots.

Citation

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Andrew Lobb. Raphael Zentner. "On spectral sequences from Khovanov homology." Algebr. Geom. Topol. 20 (2) 531 - 564, 2020. https://doi.org/10.2140/agt.2020.20.531

Information

Received: 19 November 2014; Revised: 27 May 2019; Accepted: 10 June 2019; Published: 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07195371
MathSciNet: MR4092306
Digital Object Identifier: 10.2140/agt.2020.20.531

Subjects:
Primary: 57M25

Keywords: Floer, Instanton, Khovanov

Rights: Copyright © 2020 Mathematical Sciences Publishers

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