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

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 co…