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
–invariant
(Duke Math. J. 163 (2014) 923–952), we obtain new results about the slice genera of
certain knots.
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