A vanishing identity on adjoint Reidemeister torsions of twist knots

Abstract

For a compact oriented 3-manifold with torus boundary the adjoint Reidemeister torsion is defined as a function on the ${\mathrm{SL}}_2(\mathbb{C})$-character variety depending on a choice of a boundary curve. Under reasonable assumptions, it is conjectured that the adjoint torsion satisfies a certain type of vanishing identities. In this paper, we prove that the conjecture holds for all hyperbolic twist knot exteriors by using Jacobi's residue theorem.

References in corpus (2)

• Rotating Black Hole Entropy from M5-branes
• Precision Microstate Counting for the Entropy of Wrapped M5-branes

Cited by in corpus (1)

• Adjoint Reidemeister torsions of once-punctured torus bundles