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

Lobb, Andrew

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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 sn(K). Furthermore we show that sn 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.

Citation

Lobb, A. (2012). A note on Gornik's perturbation of Khovanov-Rozansky homology. Algebraic & geometric topology, 12(1), 293-305. https://doi.org/10.2140/agt.2012.12.293

Journal Article Type Article
Publication Date Mar 12, 2012
Deposit Date Mar 16, 2012
Publicly Available Date Mar 29, 2024
Journal Algebraic and Geometric Topology
Print ISSN 1472-2747
Electronic ISSN 1472-2739
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 12
Issue 1
Pages 293-305
DOI https://doi.org/10.2140/agt.2012.12.293
Keywords Knot, Slice genus.

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