New quantum obstructions to sliceness

Lewark, Lukas Pascal; Lobb, Andrew (2016). New quantum obstructions to sliceness. Proceedings of the London Mathematical Society, 112(1), pp. 81-114. Oxford University Press 10.1112/plms/pdv068

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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 s. 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) Khovanov-Rozansky cohomology, where a perturbation gives rise to the concordance homomorphisms s_n for each n >= 2, and where we have s_2 = s. We demonstrate that s_n for n >= 3 does not in fact arise generically, and that varying the chosen perturbation gives rise both to new concordance homomorphisms as well as to new sliceness obstructions that are not equivalent to concordance homomorphisms.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Lewark, Lukas Pascal

Subjects:

500 Science > 510 Mathematics

ISSN:

0024-6115

Publisher:

Oxford University Press

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

24 Jul 2017 11:35

Last Modified:

29 Jul 2017 01:38

Publisher DOI:

10.1112/plms/pdv068

ArXiv ID:

1501.07138v2

BORIS DOI:

10.7892/boris.99753

URI:

https://boris.unibe.ch/id/eprint/99753

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