The lexicographic degree of the first two-bridge knots

Erwan Brugallé (1) , Pierre-Vincent Koseleff (2, 3, 4) , Daniel Pecker (3, 4)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
4 UPMC - Université Pierre et Marie Curie - Paris 6

We study the degree of polynomial representations of knots. We give here the lexicographic degree of all knots with eight or fewer crossings. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, isotopies on trigonal curves and explicit parametrizations obtained by perturbing a triple point.

Mots clés: Real pseudoholomorphic curves; polynomial knots; two-bridge knots; Chebyshev curves

Domaines: Topologie géométrique [math.GT]; Géométrie algébrique [math.AG]; Algorithme et structure de données [cs.DS]

Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker. The lexicographic degree of the first two-bridge knots: Extended abstract. 2014. ⟨hal-01108678v1⟩