A closed formula for the evaluation of ${\mathfrak{sl}}_N$-foams

Abstract

We give a purely combinatorial formula for evaluating closed decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral equivariant version of the ${\mathfrak{sl}}_N$ link homology categorifying the ${\mathfrak{sl}}_N$ link polynomial. We also provide connections to the equivariant cohomology rings of partial flag manifolds.

Many figures, 2 tables, Comments welcome ! Typos fixed. The computation tables were missing in v2, they are back in v3

References in corpus (2)

• Floer homology and knot complements
• Category O and sl(k) link invariants

Cited by in corpus (9)

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• Decorated one-dimensional cobordisms and tensor envelopes of noncommutative recognizable power series
• A Cohomology Theory for Planar Trivalent Graphs with Perfect Matchings
• gl(2) foams and the Khovanov homotopy type
• A cobordism category attached to Khovanov-Rozansky link homologies based on operads
• Foams, iterated wreath products, field extensions and Sylvester sums