A Steenrod square on Khovanov homology

By Robert Lipshitz, Sucharit Sarkar. 2012

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In a previous paper, we defined a space‐level version XKh(L) of Khovanov homology. This induces an action of the Steenrod algebra on Khovanov homology. In this paper, we describe the first interesting operation, Sq2:Khi,j(L)→Khi+2,j(L) . We compute this operation for all links up to 11 crossings; this, in turn, determines the stable homotopy type of XKh(L) for all such links.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c98dc1aecd4fca7a1f34b07461c36275a4dbf906