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(K). 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.

11 pages, 1 figure, proofs expanded, corollary added

References in corpus (4)

• Floer homology and knot complements
• Some differentials on Khovanov-Rozansky homology
• Computable bounds for Rasmussen's concordance invariant
• The Khovanov-Rozansky Cohomology and Bennequin Inequalities

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