On the zeroes of the Alexander polynomial of a Lorenz knot

TL;DR

This paper proves that the zeroes of the Alexander polynomial for Lorenz knots are confined within a specific annulus, with the annulus's width explicitly related to the knot's genus and braid index.

Contribution

It establishes a precise geometric bound on the zeroes of the Alexander polynomial for Lorenz knots based on their genus and braid index.

Findings

Zeroes lie within a specific annulus.

Annulus width depends explicitly on genus and braid index.

Provides a geometric constraint on polynomial zeroes.

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.