Author:
Feller Peter,Lewark Lukas,Lobb Andrew
Abstract
AbstractWe 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.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Publisher
Springer Science and Business Media LLC
Reference31 articles.
1. Baader, S.: Quasipositivity and homogeneity. Math. Proc. Camb. Philos. Soc. 139(2), 287–290 (2005)
2. Baader, S.: Slice and Gordian numbers of track knots. Osaka J. Math. 42, 257–271 (2005). arXiv:math/0504594
3. Baader, S., Ishikawa, M.: Legendrian graphs and quasipositive diagrams. Ann. Fac. Sci. Toulouse Math. (6) 18(2), 285–305 (2009). arXiv:math/0609592
4. Baader, S., Ishikawa, M.: Legendrian framings for two-bridge links. Proc. Am. Math. Soc. 139(12), 4513–4520 (2011). arXiv:0910.0355
5. Bennequin, D.: Entrelacements et équations de Pfaff. Astérisque 107–108, 87–161 (1983)