Volume 12, issue 1 (2012)

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

Andrew Lobb

Algebraic & Geometric Topology 12 (2012) 293–305
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.

Keywords
knot, slice genus
Primary: 57M25