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Computations of the Lipshitz-Sarkar Steenrod Square on Khovanov Homology

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arxiv 1210.1882 v1 pith:5AP5N6BF submitted 2012-10-05 math.GT math.AT

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keywords khovanovhomologycomputationsrefinementsquaresteenroddescribedistinct
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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.

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  1. Notes on Khovanov homology

    math.GT 2025-01 conditional

    Expository lecture notes surveying Khovanov homology, its applications, and related invariants, with no new mathematical results.

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