Adjoint Reidemeister torsions of two-bridge knots

TL;DR

This paper derives an explicit formula for the adjoint Reidemeister torsion of two-bridge knots and demonstrates its vanishing identities, advancing understanding of knot invariants.

Contribution

It provides the first explicit formula for the adjoint Reidemeister torsion of two-bridge knots and proves related vanishing identities.

Findings

Explicit formula for the torsion

Proof of vanishing identities

Enhanced understanding of knot invariants

Abstract

We give an explicit formula for the adjoint Reidemeister torsion of two-bridge knots and prove that the adjoint Reidemeister torsion satisfies a certain type of vanishing identities.