A Steenrod square on Khovanov homology

In a previous paper, we defined a space-level version X Kh ( L ) of Khovanov homology. This induces an action of the Steenrod algebra on Khovanov homology. In this paper, we describe the first interesting operation, Sq 2 : Kh i , j ( L ) → Kh i + 2 , j ( L ) . We compute this operation for all links up to 11 crossings; this, in turn, determines the stable homotopy type of X Kh ( L ) for all such links.