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

2016/07/22 by Anh T. Tran, Tran, Anh T., Yoshikazu Yamaguchi +1 · 1 citation
Mathematics · #57M27 #57M50 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1607.06628

openalex publication_date 2016/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 SL(2;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.

Cited by

• Higher dimensional twisted Alexander polynomials for metabelian representations

Related

• Higher even dimensional Reidemeister torsion for torus knot exteriors
• The twisted Reidemeister torsion of an iterated torus knot
• Reidemeister torsion and Dehn surgery on twist knots
• Non-abelian Reidemeister torsion for twist knots
• Higher dimensional twisted Alexander polynomials for metabelian representations