Volume 24, issue 2 (2020)

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

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Khovanov homotopy type, Burnside category and products

Tyler Lawson, Robert Lipshitz and Sucharit Sarkar

Geometry & Topology 24 (2020) 623–745

We give a new construction of a Khovanov stable homotopy type, or spectrum. We show that this construction gives a space stably homotopy equivalent to the Khovanov spectra constructed by Lipshitz and Sarkar  (J. Amer. Math. Soc. 27 (2014) 983–1042) and Hu, Kriz and Kriz (Topology Proc. 48 (2016) 327–360) and, as a corollary, that those two constructions give equivalent spectra. We show that the construction behaves well with respect to disjoint unions, connected sums and mirrors, verifying several of Lipshitz and Sarkar’s conjectures. Finally, combining these results with Lipshitz and Sarkar’s computations (J. Topol. 7 (2014) 817–848) and refined s–invariant (Duke Math. J. 163 (2014) 923–952), we obtain new results about the slice genera of certain knots.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

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 homotopy, Khovanov homology, flow categories
Mathematical Subject Classification 2010
Primary: 55P42, 57M25
Received: 12 May 2015
Revised: 8 January 2019
Accepted: 20 August 2019
Published: 23 September 2020
Proposed: Ciprian Manolescu
Seconded: Ralph Cohen, Ian Agol
Tyler Lawson
Department of Mathematics
University of Minnesota
Minneapolis, MN
United States
Robert Lipshitz
Department of Mathematics
University of Oregon
Eugene, OR
United States
Sucharit Sarkar
Department of Mathematics
University of California at Los Angeles
Los Angeles, CA
United States