A polynomial action on colored sl(2) link homology

Matt Hogancamp

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arXiv · 1405.2574

A polynomial action on colored sl(2) link homology

Matt Hogancamp

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Abstract

We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and categorifies a scalar-multiple of the sl(2) Reshetikhin-Turaev invariant. We expect this homology to be functorial under 4-dimensional cobordisms. The polynomial action is related to a conjecture of Gorsky-Oblomkov-Rasmussen-Shende on the stable Khovanov homology of torus knots, and as an application we obtain a weak version of this conjecture. A key new ingredient is the construction of a bounded chain complex which categorifies a scalar multiple of the Jones-Wenzl projector, in which the denominators have been cleared.

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Matt Hogancamp. 2014-05-11. A polynomial action on colored sl(2) link homology. https://arxiv.org/abs/1405.2574

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