A polynomial action on colored sl2 link homology

Hogancamp, Matthew

doi:10.4171/QT/122

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A polynomial action on colored sl₂ link homology

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Hogancamp, Matthew
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4171/QT/122
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Hogancamp, M. (2019). A polynomial action on colored sl₂ link homology. Quantum Topology, 10(1), 1-75. doi:10.4171/QT/122.

Cite as: https://hdl.handle.net/21.11116/0000-0004-82E1-A

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.