Twisted Alexander polynomial of a ribbon 2-knot of 1-fusion

Abstract

The twisted Alexander polynomial is defined as a rational function, not necessarily a polynomial. It is shown that for a ribbon 2-knot, the twisted Alexander polynomial associated to an irreducible representation of the knot group to $\mathrm{SL}(2, \mathbb{F})$ is always a polynomial. Furthermore, the twisted Alexander polynomial of a fibered ribbon 2-knot of 1-fusion has the lowest and highest degree coefficients $1$ with breadth $2m-2$, where $m$ is the breadth of its Alexander polynomial.