Finiteness of the image of the Reidemeister torsion of a splice
Annales mathématiques Blaise Pascal, Volume 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.

Published online:
DOI: 10.5802/ambp.389
Classification: 57M27, 57M25, 20C99, 14M99
Keywords: Reidemeister torsion, $A$-polynomial, character variety, splice, bending, Riley polynomial
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
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Teruaki Kitano; Yuta Nozaki. Finiteness of the image of the Reidemeister torsion of a splice. Annales mathématiques Blaise Pascal, Volume 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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