Modulo 2 Conway polynomials of rational links

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

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

We show that a polynomial is the modulo 2 Conway polynomial of a rational link if and only if it is a Fibonacci polynomial modulo 2. We deduce a simple proof of the Murasugi characterization of the modulo 2 Alexander polynomials of rational knots. We also deduce a fast algorithm to test when the Alexander polynomial of a rational knot $K$ is congruent to 1 modulo 2, which is a necessary condition for $K$ to be Lissajous.

Mots clés: Rational knots; Conway polynomials; Fibonacci polynomials; Alexander polynomials

Domaines: Topologie générale [math.GN]

Pierre-Vincent Koseleff, Daniel Pecker. Modulo 2 Conway polynomials of rational links. 2010. ⟨hal-00486065⟩