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Durham e-Theses
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Handle Cancellation in Flow Categories and the Khovanov Stable Homotopy Type

JONES, DANIEL (2015) Handle Cancellation in Flow Categories and the Khovanov Stable Homotopy Type. Doctoral thesis, Durham University.

PDF (Daniel Jones Thesis)


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_{19}, 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.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Keywords:Topology, low-dimensional topology, Khovanov homology, knots, flow category
Faculty and Department:Faculty of Science > Mathematical Sciences, Department of
Thesis Date:2015
Copyright:Copyright of this thesis is held by the author
Deposited On:04 Jun 2015 15:36

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