#### Volume 24, issue 2 (2020)

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Khovanov homotopy type, Burnside category and products

### Tyler Lawson, Robert Lipshitz and Sucharit Sarkar

Geometry & Topology 24 (2020) 623–745
##### Abstract

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.

##### Keywords
Khovanov homotopy, Khovanov homology, flow categories
##### Mathematical Subject Classification 2010
Primary: 55P42, 57M25