Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations

Abstract

A torus-covering T 2 -knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering T 2 -knot F , we determine the number of irreducible metabelian SU (2)representations of the knot group of F in terms of the Alexander polynomial of F . It is a similar result due to Lin for the knot group of a classical knot. Further, we investigate the number of irreducible metabelian SU (2)-representations using Fox's p-colorability.