Finiteness of the image of the Reidemeister torsion of a splice
Annales Mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 19-36.

The set $\mathit{RT}\left(M\right)$ of values of the $\mathrm{SL}\left(2,ℂ\right)$-Reidemeister torsion of a 3-manifold $M$ can be both finite and infinite. We prove that $\mathit{RT}\left(M\right)$ 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 :
DOI : https://doi.org/10.5802/ambp.389
Classification : 57M27,  57M25,  20C99,  14M99
Mots clés : Reidemeister torsion, $A$-polynomial, character variety, splice, bending, Riley polynomial
@article{AMBP_2020__27_1_19_0,
author = {Teruaki Kitano and Yuta Nozaki},
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},
number = {1},
year = {2020},
doi = {10.5802/ambp.389},
language = {en},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.389/}
}
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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