The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality

@article{Queffelec2014TheF,
  title={The \$\mathfrak\{sl\}\_n\$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality},
  author={Hoel Queffelec and David E. V. Rose},
  journal={arXiv: Quantum Algebra},
  year={2014}
}
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66 Citations
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66 Citations

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Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
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We show that Khovanov homology (and its sl3 variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of…
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A colored sl(N)-homology for links in S^3
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TLDR
It is proved that the homotopy type of this chain complex is invariant under Reidemeister moves and decategorifies to the Reshetikhin-Turaev sl(N) polynomial of links colored by exterior powers of the defining representation.
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