Joy Handle Cancellation in Flow Categories and the Khovanov Stable Homotopy Type free shipping

ByElle Pop

Joy Handle Cancellation in Flow Categories and the Khovanov Stable Homotopy Type free shipping

Handle Cancellation in Flow Categories and the Khovanov Stable Homotopy Type PDF (Daniel Jones Thesis) 936KbAbstractThis thesis extends classical handle cancellation occuring in Morse theory to framed flow categories. A particular framed flow category, the hermes birkin 35 replica 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.

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