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Almost positive links are strongly quasipositive

Feller, Peter; Lewark, Lukas; Lobb, Andrew

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Authors

Peter Feller

Lukas Lewark



Abstract

We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow’s in the (strong) positive. As a second main result, we give a simple and complete characterization of link diagrams with quasipositive canonical surface (the surface produced by Seifert’s algorithm). As applications, we determine which prime knots up to 13 crossings are strongly quasipositive, and we confirm the following conjecture for knots that have a canonical surface realizing their genus: a knot is strongly quasipositive if and only if the Bennequin inequality is an equality.

Citation

Feller, P., Lewark, L., & Lobb, A. (2023). Almost positive links are strongly quasipositive. Mathematische Annalen, 385(1-2), 481-510. https://doi.org/10.1007/s00208-021-02328-x

Journal Article Type Article
Acceptance Date Nov 24, 2021
Online Publication Date Jan 11, 2022
Publication Date 2023-02
Deposit Date Feb 16, 2022
Publicly Available Date Mar 3, 2023
Journal Mathematische Annalen
Print ISSN 0025-5831
Electronic ISSN 1432-1807
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 385
Issue 1-2
Pages 481-510
DOI https://doi.org/10.1007/s00208-021-02328-x
Public URL https://durham-repository.worktribe.com/output/1213673

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http://creativecommons.org/licenses/by/4.0/

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