Finiteness of the image of the Reidemeister torsion of a splice

Teruaki Kitano; Yuta Nozaki

doi:10.5802/ambp.389

Teruaki Kitano ¹ ; Yuta Nozaki ²

¹ Department of Information Systems Science, Faculty of Science and Engineering, Soka University Tangi-cho 1-236, Hachioji, Tokyo 192-8577, Japan
² Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan

Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 19-36.

Résumé

The set $RT (M)$ of values of the $SL (2, ℂ)$ -Reidemeister torsion of a 3-manifold $M$ can be both finite and infinite. We prove that $RT (M)$ is a finite set if $M$ is the splice of two certain knots in the 3-sphere. The proof is based on an observation on the character varieties and $A$ -polynomials of knots.

Publié le : 2020-08-26

DOI : 10.5802/ambp.389

Classification : 57M27, 57M25, 20C99, 14M99
Mots clés : Reidemeister torsion, $A$-polynomial, character variety, splice, bending, Riley polynomial

Affiliations des auteurs :

Teruaki Kitano ¹ ; Yuta Nozaki ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Finiteness of the image of the {Reidemeister} torsion of a splice},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {19--36},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {27},
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     year = {2020},
     doi = {10.5802/ambp.389},
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Teruaki Kitano; Yuta Nozaki. Finiteness of the image of the Reidemeister torsion of a splice. Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 19-36. doi : 10.5802/ambp.389. https://ambp.centre-mersenne.org/articles/10.5802/ambp.389/

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