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.

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

References in corpus (12)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus
• Khovanov's homology for tangles and cobordisms
• Spiders for rank 2 Lie algebras
• A functor-valued invariant of tangles
• Khovanov-Rozansky Homology and Topological Strings
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Sl(N) link homology using foams and the Kapustin-Li formula
• Category O and sl(k) link invariants
• Deformations of colored sl(N) link homologies via foams
• A geometric model for Hochschild homology of Soergel bimodules
• A characterisation of indecomposable web-modules over Khovanov-Kuperberg Algebras

Cited by in corpus (9)

• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Computer Bounds for Kronheimer-Mrowka Foam Evaluation
• A quantum categorification of the Alexander polynomial
• 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