Computations of the Lipshitz-Sarkar Steenrod Square on Khovanov Homology

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