Volume 20, issue 2 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
On spectral sequences from Khovanov homology

Andrew Lobb and Raphael Zentner

Algebraic & Geometric Topology 20 (2020) 531–564

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.

PDF Access Denied

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

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Khovanov, Floer, instanton
Mathematical Subject Classification 2010
Primary: 57M25
Received: 19 November 2014
Revised: 27 May 2019
Accepted: 10 June 2019
Published: 23 April 2020
Andrew Lobb
Department of Mathematical Sciences
Durham University
United Kingdom
Raphael Zentner
Mathematisches Institut
Universität Regensburg