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

Details A note on Gornik's perturbation of Khovanov-Rozansky homology A note on Gornik's perturbation of Khovanov-Rozansky homology

2010-12-13

arxiv.org/abs/1012.2802v2

Mathematics

Geometric Topology

11 pages, 1 figure, proofs expanded, corollary added

Scientific paper

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.

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