Algebraic & Geometric Topology 11 (2011) 2037–2106

DOI: 10.2140/agt.2011.11.2037

Abstract

We generalize the works of Lee [Adv. Math. 197 (2005) 554–586] and Gornik [arXiv math.QA/0402266] to construct a basis for generic deformations of the colored sl(N)–homology defined in [arXiv 1002.2662v2]. As applications, we construct nondegenerate pairings and co-pairings which lead to dualities of generic deformations of the colored sl(N)–homology. We also define and study colored sl(N)–Rasmussen invariants. Among other things, we observe that these invariants vanish on amphicheiral knots and discuss some implications of this observation.

Keywords

Khovanov–Rozansky homology, matrix factorization, symmetric polynomial, Rasmussen invariant, amphicheiral knot

Mathematical Subject Classification

Primary: 57M25

References

Publication

Received: 11 November 2010
Revised: 17 May 2011
Accepted: 17 May 2011
Published: 22 July 2011

Authors