Twisted Alexander polynomials of genus one two-bridge knots

Abstract

Morifuji [14] computed the twisted Alexander polynomial of twist knots for nonabelian representations. In this paper we compute the twisted Alexander polynomial and Reidemeister torsion of genus one two-bridge knots, a class of knots which includes twist knots. As an application, we give a formula for the Reidemeister torsion of the 3-manifold obtained by $\frac{1}{q}$-Dehn surgery on a genus one two-bridge knot.