On the lexicographic degree of two-bridge knots

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

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

We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp lower bound for the lexicographic degree of any knot, using real polynomial curves properties.

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

Domaines: Topologie géométrique [math.GT]; Géométrie algébrique [math.AG]; Mathématiques [math]

Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker. On the lexicographic degree of two-bridge knots. Journal of Knot Theory and Its Ramifications, 2016, 25 (7), ⟨10.1142/S0218216516500449⟩. ⟨hal-01084472v2⟩