[Sur les racines du polynome d’Alexander d’un nœud de Lorenz]
On montre que les racines du polynome d’Alexander d’un nœud de Lorenz sont situées dans un anneau dont l’épaisseur dépend explicitement du genre et de l’indice de tresse du nœud considéré.
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.
Keywords: Lorenz knot, Alexander polynomial, monodromy, surface homeomorphism
Mot clés : Nœud de Lorenz, polynome d’Alexander, monodromie, homéomorphisme de surface
@article{AIF_2015__65_2_509_0,
author = {Dehornoy, Pierre},
title = {On the zeroes of the {Alexander} polynomial of a {Lorenz} knot},
journal = {Annales de l'Institut Fourier},
pages = {509--548},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {65},
number = {2},
year = {2015},
doi = {10.5802/aif.2938},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2938/}
}
TY - JOUR AU - Dehornoy, Pierre TI - On the zeroes of the Alexander polynomial of a Lorenz knot JO - Annales de l'Institut Fourier PY - 2015 SP - 509 EP - 548 VL - 65 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2938/ DO - 10.5802/aif.2938 LA - en ID - AIF_2015__65_2_509_0 ER -
%0 Journal Article %A Dehornoy, Pierre %T On the zeroes of the Alexander polynomial of a Lorenz knot %J Annales de l'Institut Fourier %D 2015 %P 509-548 %V 65 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2938/ %R 10.5802/aif.2938 %G en %F AIF_2015__65_2_509_0
Dehornoy, Pierre. On the zeroes of the Alexander polynomial of a Lorenz knot. Annales de l'Institut Fourier, Tome 65 (2015) no. 2, pp. 509-548. doi : 10.5802/aif.2938. http://www.numdam.org/articles/10.5802/aif.2938/
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