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arXiv · 1405.5920

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

Hoel Queffelec·David E. V. Rose
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Abstract

We give a purely combinatorial construction of colored $\mathfrak{sl}_n$ link homology. The invariant takes values in a 2-category where 2-morphisms are given by foams, singular cobordisms between $\mathfrak{sl}_n$ webs; applying a (TQFT-like) representable functor recovers (colored) Khovanov-Rozansky homology. Novel features of the theory include the introduction of `enhanced' foam facets which fix sign issues associated with the original matrix factorization formulation and the use of skew Howe duality to show that (enhanced) closed foams can be evaluated in a completely combinatorial manner. The latter answers a question posed in math.GT/0708.2228.

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Hoel Queffelec, David E. V. Rose. 2014-05-22. The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality. https://arxiv.org/abs/1405.5920

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