On Alexander-Conway polynomials of two-bridge links

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

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

We consider Conway polynomials of two-bridge links as Euler continuant polynomials. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley on Alexander polynomials. 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. We easily obtain some bounds for the roots of the Alexander polynomials of two-bridge links.

Mots clés: Euler continuant polynomial; two-bridge link; Conway polynomial; Alexander polynomial

Domaines: Topologie géométrique [math.GT]

Pierre-Vincent Koseleff, Daniel Pecker. On Alexander-Conway polynomials of two-bridge links. 2012. ⟨hal-00778808v1⟩