A Steenrod Square on Khovanov Homology

Details A Steenrod Square on Khovanov Homology A Steenrod Square on Khovanov Homology

2012-04-25

arxiv.org/abs/1204.5776v1

Mathematics

Geometric Topology

46 pages, 6 figures. Includes table of homotopy types for links up to 11 crossings

Scientific paper

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.

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