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

  • 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 Reidemeister torsion, graph manifold, asymptotic behavior, exceptional surgery
MSC Classifications: 57M27, 57M50 show english descriptions Invariants of knots and 3-manifolds
Geometric structures on low-dimensional manifolds
57M27 - Invariants of knots and 3-manifolds
57M50 - Geometric structures on low-dimensional manifolds
 

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