A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

[Une relation entre la torsion de Reidemeister non acyclique et un zéro de la torsion de Reidemeister acyclique]

Yamaguchi, Yoshikazu

Annales de l'Institut Fourier, Tome 58 (2008), p. 337-362 / Harvested from Numdam

Résumé

Nous montrons une relation entre la torsion de Reidemeister non-acyclique et un zéro de la torsion de Reidemeister acyclique pour une représentation $\lambda $-régulière dans ${\rm SU}(2)$ ou ${\rm SL}(2, \mathbb{C})$ 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 ${\rm SU}(2)$-représentations du groupe du nœud.

Abstract

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a $\lambda $-regular ${\rm SU}(2)$ or ${\rm SL}(2, \mathbb{C})$-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 $2$-bridge knot and ${\rm SU}(2)$-representations of its knot group.

Détail

Publié le : 2008-01-01

MR 2401224 | Zbl 1158.57027

DOI : https://doi.org/10.5802/aif.2352
Classification:  57Q10,  57M05,  57M27
Mots clés: torsion de Reidemeister, invariant tordu de Alexander, nœuds, variétés des représentations

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