An orientation for the SU(2)-representation space of knot groups

The aim of this paper is to study the SU(2)-representation spaces of knot groups. For a given a knot k⊂S3 we denote by R(k) the space of equivalence classes of irreducible representations of the knot group π1(S3⧹k) in SU(2) and we denote by Reg(k)⊂R(k) the space of regular representations. It is well known that Reg(k)⊂R(k) is a real one-dimensional manifold. in result of this paper is to prove that Reg(k) also carries a cannonical orientation. As an application we are able to explain a generalization of a result of X.-S. Lin concerning the knot signatures.