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On Alexander-Conway polynomials of two-bridge links

By Pierre-Vincent Koseleff and Daniel Pecker

Abstract

18 p.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

Topics: Euler continuant polynomial, two-bridge link, Conway polynomial, Alexander polynomial, 57M25, 11C08, [ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]
Publisher: HAL CCSD
Year: 2013
OAI identifier: oai:HAL:hal-00778808v2
Provided by: Hal-Diderot

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