Adjoint Reidemeister torsions of once-punctured torus bundles

TL;DR

This paper provides new evidence supporting a conjecture on the vanishing of adjoint Reidemeister torsions in hyperbolic 3-manifolds, specifically for once-punctured torus bundles with tunnel number one.

Contribution

It proves the vanishing identity for all hyperbolic once-punctured torus bundles with tunnel number one and shows it does not hold for torus knot exteriors.

Findings

Vanishing identity holds for all hyperbolic once-punctured torus bundles with tunnel number one.

The vanishing identity does not hold for any torus knot exteriors.

Provides infinitely many new supporting examples for the conjecture.

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.