On the quantum filtration of the Khovanov-Rozansky cohomology

Abstract

We prove the quantum filtration on the Khovanov-Rozansky link cohomology H_p with a general degree (n+1) monic potential polynomial p(x) is invariant under Reidemeister moves, and construct a spectral sequence converging to H_p that is invariant under Reidemeister moves, whose E_1 term is isomorphic to the Khovanov-Rozansky sl(n)-cohomology H_n. Then we define a generalization of the Rasmussen invariant, and study some of its properties. We also discuss relations between upper bounds of the self-linking number of transversal links in the standard contact three sphere.