A Steenrod Square on Khovanov Homology

Robert Lipshitz; Sucharit Sarkar

doi:10.1112/jtopol/jtu005

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arXiv · 1204.5776

A Steenrod Square on Khovanov Homology

Robert Lipshitz·Sucharit Sarkar

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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.

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Robert Lipshitz, Sucharit Sarkar. 2012-04-25. A Steenrod Square on Khovanov Homology. https://doi.org/10.1112/jtopol%2Fjtu005

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