A Khovanov stable homotopy type

Abstract

Given a link diagram L we construct spectra X^j(L) so that the Khovanov homology Kh^{i,j}(L) is isomorphic to the (reduced) singular cohomology H^i(X^j(L)). The construction of X^j(L) is combinatorial and explicit. We prove that the homotopy type of X^j(L) depends only on the isotopy class of the corresponding link.

68 pages. V5: updated to accepted version. V6: fix typesetting bug in figures introduced in V5

References in corpus (5)

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• Computations of the Lipshitz-Sarkar Steenrod Square on Khovanov Homology
• Field theories, stable homotopy theory and Khovanov homology
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Cited by in corpus (35)

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• Framed cobordism and flow category moves
• Morse-Bott cohomology from homological perturbation theory
• A hitchhiker's guide to Khovanov homology
• Categorical lifting of the Jones polynomial: a survey
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• A fast algorithm for calculating $s$-invariants
• Steenrod square for virtual links toward Khovanov-Lipshitz-Sarkar stable homotopy type for virtual links
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• Homotopy functoriality for Khovanov spectra
• A knot Floer stable homotopy type
• Khovanov-Lipshitz-Sarkar homotopy type for links in thickened higher genus surfaces
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• An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2
• Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras
• Towards an ${\mathfrak{sl}}_2$ action on the annular Khovanov spectrum
• Non-Trivial Steenrod Squares on Prime, Hyperbolic and Satellite Knots