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, p. 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 : https://doi.org/10.5802/aif.2352
Classification:  57Q10,  57M05,  57M27
Mots clés: torsion de Reidemeister, invariant tordu de Alexander, nœuds, variétés des représentations
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {1},
     year = {2008},
     pages = {337-362},
     doi = {10.5802/aif.2352},
     mrnumber = {2401224},
     zbl = {1158.57027},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_2008__58_1_337_0/

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