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Title: Handle cancellation in flow categories and the Khovanov stable homotopy type
Author: Jones, Daniel
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2015
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This thesis extends classical handle cancellation occuring in Morse theory to framed flow categories. A particular framed flow category, the Khovanov flow category, was defined by Lipshitz-Sarkar in [LS14a] where they construct a Khovanov stable homotopy type. This stable homotopy tye induces a Steenrod square on Khovanov homology, and a result by Baues [Bau95] shows that this is enough to completely determine the Khovanov stable homotopy type of relatively simple links. This includes all links with up to 11 crossings, and [LS14b] provides a list of the stable homotopy types for all such links. The first knot for which these computations are non-trival is 8?, and the calculations for the Steenrod square of this knot can be simplified drastically using handle cancellation in framed flow categories. The thesis concludes by exhibiting this simplification.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available