Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor
Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor
Patrick Orson
Professor Dirk Schuetz dirk.schuetz@durham.ac.uk
Professor
The Lipshitz–Sarkar stable homotopy link invariant defines Steenrod squares on the Khovanov cohomology of a link. Lipshitz–Sarkar constructed an algorithm for computing the first two Steenrod squares. We develop a new algorithm which implements the flow category simplification techniques previously defined by the authors and Dan Jones. We give a purely combinatorial approach to calculating the second Steenrod square and Bockstein homomorphisms in Khovanov cohomology, and flow categories in general. The new method has been implemented in a computer program by the third author and applied to large classes of knots and links. Several homotopy types not previously witnessed are observed, and more evidence is obtained that Khovanov stable homotopy types do not contain CP2 as a wedge summand. In fact, we are led by our calculations to formulate an even stronger conjecture in terms of Z/2 summands of the cohomology.
Lobb, A., Orson, P., & Schuetz, D. (2020). Khovanov homotopy calculations using flow category calculus. Experimental Mathematics, 29(4), 475-500. https://doi.org/10.1080/10586458.2018.1482805
Journal Article Type | Article |
---|---|
Acceptance Date | May 29, 2018 |
Online Publication Date | Apr 9, 2019 |
Publication Date | 2020 |
Deposit Date | Jun 1, 2018 |
Publicly Available Date | Apr 9, 2020 |
Journal | Experimental Mathematics |
Print ISSN | 1058-6458 |
Electronic ISSN | 1944-950X |
Publisher | Taylor and Francis Group |
Peer Reviewed | Peer Reviewed |
Volume | 29 |
Issue | 4 |
Pages | 475-500 |
DOI | https://doi.org/10.1080/10586458.2018.1482805 |
Public URL | https://durham-repository.worktribe.com/output/1329654 |
Accepted Journal Article
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Copyright Statement
This is an Accepted Manuscript of an article published by Taylor & Francis in Experimental Mathematics on 09 April 2019 available online: http://www.tandfonline.com/10.1080/10586458.2018.1482805
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