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# The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots

Published:2017-05-24
Printed: Mar 2018
• Anh T. Tran,
Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, USA
• Yoshikazu Yamaguchi,
Department of Mathematics, Akita University, 1-1 Tegata-Gakuenmachi, Akita, 010-8502, Japan
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## Abstract

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 $\operatorname{SL}_2(\mathbb{C})$-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 coefficients in the higher dimensional Reidemeister torsion explicitly.
 Keywords: Reidemeister torsion, graph manifold, asymptotic behavior, exceptional surgery
 MSC Classifications: 57M27 - Invariants of knots and 3-manifolds 57M50 - Geometric structures on low-dimensional manifolds

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