EQUIVARIANT COLORED 𝔰𝔩(N)-HOMOLOGY FOR LINKS

Abstract

In this sequel to [A colored 𝔰𝔩(N)-homology for links in S3, preprint (2009), arXiv:0907.0695v5], we construct an equivariant colored 𝔰𝔩(N)-homology for links, which generalizes both the above mentioned paper and the paper by [D. Krasner, Equivariant sl(n)-link homology, preprint (2008), arXiv:0804.3751v2]. The construction is a straightforward generalization of the paper, [A colored 𝔰𝔩(N)-homology for links in S3]. The proof of invariance is based on a simple observation which allows us to translate the proof in the above mentioned paper 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 in the papers by [B. Gornik, Note on Khovanov link cohomology, preprint (2004), arXiv:math.QA/0402266 and E. Lee, An endomorphism of the Khovanov invariant, Adv. Math.197(2) (2005) 554–586].