Equivariant colored sl(N)-homology for links

Abstract

We construct an equivariant colored sl(N)-homology for links, which generalizes both the colored sl(N)-homology defined by the author and the equivariant sl(N)-homology defined by Krasner. The construction is a straightforward generalization of that of the colored sl(N)-homology. The proof of invariance is based on a simple observation which allows us to translate the proof of the invariance of the colored sl(N)-homology into the new setting. As an application, we prove that deformations over C of the colored sl(N)-homology are link invariants. We also construct a spectral sequence connecting the colored sl(N)-homology to its deformations over C, which generalizes the spectral sequence given by Lee and Gornik.

83 pages, many figures

References in corpus (5)

• Knot homology groups from instantons
• A colored sl(N)-homology for links in S^3
• Some differentials on Khovanov-Rozansky homology
• A slice genus lower bound from sl(n) Khovanov-Rozansky homology
• Equivariant sl(n)-link homology

Cited by in corpus (10)

• A colored sl(N)-homology for links in S^3
• Deformations of colored sl(N) link homologies via foams
• Annular Evaluation and Link Homology
• Generic deformations of the colored sl(N)-homology for links
• A diagrammatic categorification of the q-Schur algebra
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Colored sl(N) link homology via matrix factorizations
• Simplified Khovanov-Rozansky Chain Complexes of Open 2-braids
• Curved Rickard complexes and link homologies
• Equivariant Khovanov-Rozansky Homology and Lee-Gornik Spectral Sequence