[Une relation entre la torsion de Reidemeister non acyclique et un zéro de la torsion de Reidemeister acyclique]
Nous montrons une relation entre la torsion de Reidemeister non-acyclique et un zéro de la torsion de Reidemeister acyclique pour une représentation -régulière dans ou du groupe d’un nœud. Alors nous pouvons donner une méthode pour calculer la torsion de Reidemeister non-acyclique de l’extérieur d’un nœud. Nous calculons un nouvel exemple et étudions le comportement de la torsion de Reidemeister non-acyclique associée à un nœud à deux-ponts et une -représentations du groupe du nœud.
We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a -regular or -representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a -bridge knot and -representations of its knot group.
Keywords: Reidemeister torsion, twisted Alexander invariant, knots, representation spaces
Mot clés : torsion de Reidemeister, invariant tordu de Alexander, nœuds, variétés des représentations
Yamaguchi, Yoshikazu 1
@article{AIF_2008__58_1_337_0,
author = {Yamaguchi, Yoshikazu},
title = {A relationship between the non-acyclic {Reidemeister} torsion and a zero of the acyclic {Reidemeister} torsion},
journal = {Annales de l'Institut Fourier},
pages = {337--362},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {58},
number = {1},
year = {2008},
doi = {10.5802/aif.2352},
mrnumber = {2401224},
zbl = {1158.57027},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2352/}
}
TY - JOUR AU - Yamaguchi, Yoshikazu TI - A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion JO - Annales de l'Institut Fourier PY - 2008 SP - 337 EP - 362 VL - 58 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2352/ DO - 10.5802/aif.2352 LA - en ID - AIF_2008__58_1_337_0 ER -
%0 Journal Article %A Yamaguchi, Yoshikazu %T A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion %J Annales de l'Institut Fourier %D 2008 %P 337-362 %V 58 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2352/ %R 10.5802/aif.2352 %G en %F AIF_2008__58_1_337_0
Yamaguchi, Yoshikazu. A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion. Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 337-362. doi : 10.5802/aif.2352. https://aif.centre-mersenne.org/articles/10.5802/aif.2352/
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