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

By Hoel Queffelec, David E. V. Rose. 2014

95 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6aafb93f17f24ee0d694e375b567175f01c90c9f

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In Geometry and Topology

1. Michael Ehrig
2. D. Tubbenhauer
3. Paul Wedrich

In Mathematical Physics

1. Michael Ehrig
2. D. Tubbenhauer
3. Paul Wedrich

Citations in the corpus

• Functoriality of colored link homologies (2017, methodology): “Queffelec–Rose [42, Section 4.3] have provided proofs for the Reidemeister moves that we will call (R2+) and (R3+) (see Section 3.3) for all colors.”