An orientation for the [formula omitted]-representation space of knot groups

Abstract

The aim of this paper is to study the SU(2) -representation spaces of knot groups. For a given a knot k⊂S 3 we denote by R(k) the space of equivalence classes of irreducible representations of the knot group π 1(S 3⧹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. The main 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.