Computations of the Lipshitz-Sarkar Steenrod Square on Khovanov Homology

Abstract

Lipshitz and Sarkar recently introduced a space-level refinement of Khovanov homology. This refinement induces a Steenrod square operation $\Sq^2$ on Khovanov homology which they describe explicitly. This paper presents some computations of $\Sq^2$. In particular, we give examples of links with identical integral Khovanov homology but with distinct Khovanov homotopy types.

13 pages. Includes table of computations

References in corpus (3)

• Khovanov Homology and Conway Mutation
• Odd Khovanov homology is mutation invariant
• Mutation invariance of Khovanov homology over ${\mathbb{F}}_2$

Cited by in corpus (6)

• On Khovanov Homology and Related Invariants
• Homotopy functoriality for Khovanov spectra
• Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras
• Khovanov-Lipshitz-Sarkar homotopy type for links in thickened surfaces
• A Bar-Natan homotopy type
• Towards an ${\mathfrak{sl}}_2$ action on the annular Khovanov spectrum