On the zeroes of the Alexander polynomial of a Lorenz knot

Abstract

We show that the zeroes of the Alexander polynomial of a Lorenz knot all lie in some annulus whose width depends explicitly on the genus and the braid index of the considered knot.

30p., final version, to appear in Ann. Inst. Fourier

References in corpus (6)

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• Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid
• Les noeuds de Lorenz
• Small dilatation pseudo-Anosovs and 3-manifolds
• Polynomial invariants of pseudo-Anosov maps
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• Modular links: Bunch algorithm and upper volume bounds
• Checkerboard graph links and simply laced Dynkin diagrams
• The $p$-adic limits of class numbers in ${\mathbb{Z}}_p$-towers
• Linking numbers of modular knots
• On the signature of a positive braid