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 SL(2 , F ) is always a polynomial. Further-more, the twisted Alexander polynomial of a fibered ribbon 2-knot of 1-fusion has the lowest and highest degree coe ffi cients 1 with breadth 2 m − 2, where m is the breadth of its Alexander polynomial.