Khovanov homotopy type, burnside category and products

Tyler Lawson, Robert Lipshitz, Sucharit Sarkar

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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.

Original languageEnglish (US)
Pages (from-to)623-745
Number of pages123
JournalGeometry and Topology
Issue number2
StatePublished - 2020

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