Almost positive links are strongly quasipositive
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 DOI:
 10.48550/arXiv.1809.06692
 arXiv:
 arXiv:1809.06692
 Bibcode:
 2018arXiv180906692F
 Keywords:

 Mathematics  Geometric Topology;
 57M25
 EPrint:
 25 pages, 11 figures, comments welcome! v2: Added 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 iff the Bennequin inequality is an equality. v3: Some restructuring and added details. Accepted by Mathematische Annalen