On the zeroes of the Alexander polynomial of a Lorenz knot

2011/10/31 by Pierre Dehornoy
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Alexander polynomial #Braid #Combinatorics #Discrete mathematics #Geometric and Algebraic Topology #HOMFLY polynomial #Jones polynomial #Knot (papermaking) #Knot invariant #Knot polynomial #Knot theory #Mathematical analysis #Mathematics #Matrix polynomial #Polynomial #Pure mathematics #Square-free polynomial #Trefoil knot #math.DS #math.GT #semigroups and automata theory

paper · pdf · doi:10.5802/aif.2938

published as Annales de l'institut Fourier 65 (2015), 509-548 · 30p., final version, to appear in Ann. Inst. Fourier

arxiv created 2014/07/16 · openalex publication_date 2015/07/23 · arxiv updated 2016/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Small dilatation pseudo-Anosovs and 3-manifolds
• On the geometry and dynamics of diffeomorphisms of surfaces
• Knotted periodic orbits in dynamical systems—I: Lorenz's equation
• A family of pseudo-Anosov braids with small dilatation
• Speculations Concerning the Range of Mahler's Measure
• Deterministic Nonperiodic Flow
• Salem-Boyd sequences and Hopf plumbing
• Lehmer's question, knots and surface dynamics