A note on Gornik’s perturbation of Khovanov–Rozansky homology

Lobb, Andrew

doi:10.2140/agt.2012.12.293

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

Andrew Lobb

Algebraic & Geometric Topology 12 (2012) 293–305

DOI: 10.2140/agt.2012.12.293

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.

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/

Volume 12, issue 1 (2012)