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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 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.

Keywords
knot, slice genus
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 6 October 2011
Accepted: 6 November 2011
Published: 12 March 2012
Authors
Andrew Lobb
Department of Mathematical Sciences
Durham University
Science Laboratories
South Road
Durham
DH1 3LE
UK
http://www.maths.dur.ac.uk/~ddmb48/