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Almost positive links are strongly quasipositive.

Feller, Peter and Lewark, Lukas and Lobb, Andrew (2022) 'Almost positive links are strongly quasipositive.', Mathematische annalen. .

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00208-021-02328-x
Publisher statement:This 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.
Date accepted:24 November 2021
Date deposited:17 February 2022
Date of first online publication:11 January 2022
Date first made open access:17 February 2022

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