Adjoint twisted Alexander polynomials of genus one two-bridge knots

TL;DR

This paper provides explicit formulas for the adjoint twisted Alexander polynomial and nonabelian Reidemeister torsion specifically for genus one two-bridge knots, advancing the understanding of their topological invariants.

Contribution

It introduces explicit formulas for key invariants of genus one two-bridge knots, a novel contribution to knot theory.

Findings

Explicit formulas for adjoint twisted Alexander polynomial

Explicit formulas for nonabelian Reidemeister torsion

Enhanced understanding of genus one two-bridge knots

Abstract

We give explicit formulas for the adjoint twisted Alexander polynomial and the nonabelian Reidemeister torsion of genus one two-bridge knots.