Conway polynomials of two-bridge links

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

1 LIP6 - Laboratoire d'Informatique de Paris 6
2 SALSA - Solvers for Algebraic Systems and Applications
3 UPMC - Université Pierre et Marie Curie - Paris 6

We give necessary conditions for the Conway polynomial of a two-bridge link. We apply our conditions to the Alexander polynomial of a two-bridge knot, and obtain simple proofs of the classical theorems of Murasugi and Hartley. We also give sharp bounds for the coefficients of the Conway and Alexander polynomials of a two-bridge link. These bounds improve and generalize those of Nakanishi and Suketa. The efficiency of these conditions are compared on a large number of knots and links.

Mots clés: Two-bridge link; Conway polynomial; Alexander polynomial

Domaines: Topologie géométrique [math.GT]

Pierre-Vincent Koseleff, Daniel Pecker. Conway polynomials of two-bridge links. 2010. ⟨hal-00538729v1⟩