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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. .


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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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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