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The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots

Published online by Cambridge University Press:  20 November 2018

Anh T. Tran  and
Yoshikazu Yamaguchi
Anh T. Tran
Affiliation:
Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, USA, e-mail: att140830@utdallas.edu
Yoshikazu Yamaguchi
Affiliation:
Department of Mathematics, Akita University, 1-1 Tegata-Gakuenmachi, Akita, 010-8502, Japan, e-mail: shouji@math.akita-u.ac.jp
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Abstract

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We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible $\text{S}{{\text{L}}_{2}}(\mathbb{C})$-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We also give the set of the limits of the leading coeõcients in the higher dimensional Reidemeister torsion explicitly.

Keywords

57M2757M50Reidemeister torsiongraph manifoldasymptotic behaviorexceptional surgery
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 211 - 224
Copyright
Copyright © Canadian Mathematical Society 2018

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