Almost positive links are strongly quasipositive

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 su...

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Detalles Bibliográficos
Autores principales: Feller, Peter, Lewark, Lukas, Lobb, Andrew
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9889511/
https://www.ncbi.nlm.nih.gov/pubmed/36744241
http://dx.doi.org/10.1007/s00208-021-02328-x
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author Feller, Peter
Lewark, Lukas
Lobb, Andrew
author_facet Feller, Peter
Lewark, Lukas
Lobb, Andrew
author_sort Feller, Peter
collection PubMed
description 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.
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spelling pubmed-98895112023-02-02 Almost positive links are strongly quasipositive Feller, Peter Lewark, Lukas Lobb, Andrew Math Ann Article 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. Springer Berlin Heidelberg 2022-01-11 2023 /pmc/articles/PMC9889511/ /pubmed/36744241 http://dx.doi.org/10.1007/s00208-021-02328-x Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Feller, Peter
Lewark, Lukas
Lobb, Andrew
Almost positive links are strongly quasipositive
title Almost positive links are strongly quasipositive
title_full Almost positive links are strongly quasipositive
title_fullStr Almost positive links are strongly quasipositive
title_full_unstemmed Almost positive links are strongly quasipositive
title_short Almost positive links are strongly quasipositive
title_sort almost positive links are strongly quasipositive
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9889511/
https://www.ncbi.nlm.nih.gov/pubmed/36744241
http://dx.doi.org/10.1007/s00208-021-02328-x
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