#### Volume 20, issue 2 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
On spectral sequences from Khovanov homology

### Andrew Lobb and Raphael Zentner

Algebraic & Geometric Topology 20 (2020) 531–564
##### 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 $\left(4,5\right)$–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.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 44.192.65.228 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.