Modulo 2 Conway polynomials of rational links

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00486065
Contributor : Pierre-Vincent Koseleff <>
Submitted on : Monday, May 24, 2010 - 9:07:02 PM
Last modification on : Thursday, March 21, 2019 - 2:41:41 PM
Long-term archiving on: Thursday, September 16, 2010 - 3:03:03 PM

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

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