Almost positive links are strongly quasipositive

Peter Feller; Lukas Lewark; Andrew Lobb

doi:10.1007/s00208-021-02328-x

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arXiv · 1809.06692

Almost positive links are strongly quasipositive

Peter Feller·Lukas Lewark·Andrew Lobb

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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 simple and complete characterizations 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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Peter Feller, Lukas Lewark, Andrew Lobb. 2018-09-18. Almost positive links are strongly quasipositive. https://doi.org/10.1007/s00208-021-02328-x

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