Finiteness of the image of the Reidemeister torsion of a splice

The set \(\mathit{RT}(M)\) of values of the \(\mathit{SL}(2,\mathbb{C})\)-Reidemeister torsion of a 3-manifold \(M\) can be both finite and infinite. We prove that \(\mathit{RT}(M)\) 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...

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Bibliographic Details
Published inarXiv.org
Main Authors Kitano, Teruaki, Nozaki, Yuta
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.05.2020
Subjects
Knots
Mathematics - Geometric Topology
Polynomials
Torsion
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Summary:The set \(\mathit{RT}(M)\) of values of the \(\mathit{SL}(2,\mathbb{C})\)-Reidemeister torsion of a 3-manifold \(M\) can be both finite and infinite. We prove that \(\mathit{RT}(M)\) 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.02559