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

Lobb, Andrew

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: Feb 18, 2014
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1509487