A note on Gornik's perturbation of Khovanov–Rozansky homology

Abstract

We show that the information contained in the associated graded vector space to Gornik’s version of Khovanov–Rozansky knot homology is equivalent to a single even integer $s_n\left(K\right)$. Furthermore we show that $s_n$ is a homomorphism from the smooth knot concordance group to the integers. This is in analogy with Rasmussen’s invariant coming from a perturbation of Khovanov homology.