Conway polynomials of two-bridge links

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

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 SALSA - Solvers for Algebraic Systems and Applications

We give necessary conditions for a polynomial to be the Conway polynomial of a two-bridge link. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley. We give a modulo 2 congruence for links, which implies the classical modulo 2 Murasugi congruence for knots. 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.

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-00538729v2⟩