On Alexander-Conway polynomials of two-bridge linksReport as inadecuate

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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 Inria Paris-Rocquencourt

Abstract : We consider Conway polynomials of two-bridge links as Euler continuant polynomials. As a consequence, we obtain new and elementary proofs of classical Murasugi-s 1958 alternating theorem and Hartley-s 1979 trapezoidal theorem. We give a modulo 2 congruence for links, which implies the classical Murasugi-s 1971 congruence for knots. We also give sharp bounds for the coefficients of Euler continuants and deduce bounds for the Alexander polynomials of two-bridge links. These bounds improve and generalize those of Nakanishi Suketa-96. We easily obtain some bounds for the roots of the Alexander polynomials of two-bridge links. This is a partial answer to Hoste-s conjecture on the roots of Alexander polynomials of alternating knots.

Keywords : Euler continuant polynomial two-bridge link Conway polynomial Alexander polynomial

Author: Pierre-Vincent Koseleff - Daniel Pecker -

Source: https://hal.archives-ouvertes.fr/


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