Irreducible S L (2,-metabelian representations of branched twist spins

An (m,n)-branched twist spin is a fibered 2-knot in S4 which is determined by a 1-knot K and coprime integers m and n. For a 1-knot, Nagasato proved that the number of conjugacy classes of irreducible SL(2, )-metabelian representations of the knot group of a 1-knot is determined by the knot determinant of the 1-knot. In this paper, we prove that the number of irreducible SL(2,)-metabelian representations of the knot group of an (m,n)-branched twist spin is determined up to conjugation by the determinant of the associated 1-knot in the orbit space by comparing a presentation of the knot group of the branched twist spin with the Lin's presentation of the knot group of the 1-knot.