A Steenrod Square on Khovanov Homology

Abstract

In a previous paper, we defined a space-level version X(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(L) for all such links.

45 pages, 6 figures. Includes table of Khovanov homotopy types for links up to 11 crossings. Accepted for publication by the Journal of Topology, although the final published version will have different formatting and might have different theorem numbering

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