Twisted Alexander polynomials of tunnel number one Montesinos knots

Abstract

We calculate the twisted Alexander polynomials of all tunnel number one Montesinos knots associated to their $S{L}_2(\mathbb{C})$-representations and obtain their leading coefficients and degrees. As a corollary, we get some interesting examples, that is, nonfibered knots with monic Alexander polynomials which have non-monic twisted Alexander polynomials.

33 pages, 9 figures

References in corpus (1)

• Twisted Alexander polynomials of 2-bridge knots for parabolic representations