New Quantum Obstructions to Sliceness

Lewark, Lukas; Lobb, Andrew

doi:10.1112/plms/pdv068

New Quantum Obstructions to Sliceness

Lewark, Lukas; Lobb, Andrew

Authors

Lukas Lewark

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

Abstract

It is well known that generic perturbations of the complex Frobenius algebra used to define Khovanov cohomology each give rise to Rasmussen's concordance invariant ss. This gives a concordance homomorphism to the integers and a strong lower bound on the smooth slice genus of a knot. Similar behavior has been observed in sl(n)sl(n) Khovanov–Rozansky cohomology, where a perturbation gives rise to the concordance homomorphisms snsn for each n≥2n≥2, and where we have s2=ss2=s. We demonstrate that snsn for n≥3n≥3 does not in fact arise generically, and that varying the chosen perturbation gives rise both to new concordance homomorphisms and to new sliceness obstructions that are not equivalent to concordance homomorphisms.

Citation

Lewark, L., & Lobb, A. (2016). New Quantum Obstructions to Sliceness. Proceedings of the London Mathematical Society, 112(1), 81-114. https://doi.org/10.1112/plms/pdv068

Journal Article Type	Article
Acceptance Date	Aug 19, 2015
Online Publication Date	Feb 5, 2016
Publication Date	Jan 1, 2016
Deposit Date	Aug 31, 2015
Publicly Available Date	Sep 7, 2015
Journal	Proceedings of the London Mathematical Society
Print ISSN	0024-6115
Electronic ISSN	1460-244X
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	112
Issue	1
Pages	81-114
DOI	https://doi.org/10.1112/plms/pdv068

Files

Accepted Journal Article (802 Kb)
PDF

Copyright Statement
© 2016 Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.