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]
Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 337-362.

Nous montrons une relation entre la torsion de Reidemeister non-acyclique et un zéro de la torsion de Reidemeister acyclique pour une représentation λ-régulière dans SU (2) ou SL (2,) 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 SU (2)-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 λ-regular SU (2) or SL (2,)-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 SU (2)-representations of its knot group.

DOI : 10.5802/aif.2352
Classification : 57Q10, 57M05, 57M27
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

1 University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba Meguro Tokyo 153-8914 (Japan)
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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. http://www.numdam.org/articles/10.5802/aif.2352/

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