Deformations of colored sl(N) link homologies via foams

Abstract

We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology to give a completely combinatorial construction of Wu's deformed colored sl(N) link homologies. By studying the underlying deformed higher representation theoretic structures and generalizing the Karoubi envelope approach of Bar-Natan and Morrison we explicitly compute the deformed invariants in terms of undeformed type A link homologies of lower rank and color.

64 pages, many figures

References in corpus (6)

• 2-Kac-Moody algebras
• Derived equivalences for symmetric groups and sl\_2-categorification
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Rigidity in higher representation theory
• Equivariant colored sl(N)-homology for links
• Khovanov-Rozansky homology via Cohen-Macaulay approximations and Soergel bimodules

Cited by in corpus (20)

• Functoriality of colored link homologies
• A closed formula for the evaluation of ${\mathfrak{sl}}_N$-foams
• Annular Evaluation and Link Homology
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Towards tangle calculus for Khovanov polynomials
• Upsilon-like concordance invariants from sl(n) knot cohomology
• Generic ${\mathfrak{gl}}_2$-foams, web and arc algebras
• Planar decomposition of bipartite HOMFLY polynomials in symmetric representations
• Decorated one-dimensional cobordisms and tensor envelopes of noncommutative recognizable power series
• Anchored foams and annular homology
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Curved Rickard complexes and link homologies
• On webs in quantum type $C$
• gl(2) foams and the Khovanov homotopy type
• Categorification of the internal braid group action for quantum groups I: 2-functoriality
• Transverse link invariants from the deformations of Khovanov ${\mathfrak{sl}}_3$-homology
• Foams, iterated wreath products, field extensions and Sylvester sums
• A skein relation for singular Soergel bimodules
• Link splitting deformation of colored Khovanov--Rozansky homology