Adjoint Reidemeister torsions of once-punctured torus bundles

2021/09/15 by Anh T. Tran, Tran, Anh T., Yoshikazu Yamaguchi +1
Mathematics · #57K31 (Primary) 57K32(Secondary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2109.07058

openalex publication_date 2021/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gang, Kim and Yoon have recently proposed a conjecture on a vanishing identity of adjoint Reidemeister torsions of hyperbolic 3-manifolds with torus boundary, from the viewpoint of wrapped M5-branes. In this paper, we provide infinitely many new supporting examples to this conjecture. These examples come from hyperbolic once-punctured torus bundles. We show that the vanishing identity holds for all hyperbolic once-punctured torus bundles with tunnel number one. We also show the vanishing identity does not hold for any torus knot exteriors.

Related

• The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admit a Unique Decomposition
• Adjoint twisted Reidemeister torsion and Gram matrices
• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
• Higher even dimensional Reidemeister torsion for torus knot exteriors
• Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsion