Unitary representations of knot groups (Q2367219)

The paper is a part of the author's program to develop a generalization of Casson's invariant by using \(\text{SU}(n)\) instead of \(\text{SU}(2)\). The first step in such a program is to define an analog of Casson's invariant of knots. The definition of these invariants and the derivation of their properties is given in [the author and \textit{D. D. Long}, Casson's invariant and surgery on knots, Proc. Edinb. Math. Soc., II. Ser. 35, No. 3, 383-395 (1992; Zbl 0764.57010) and the author and \textit{A. Nicas}, An intersection homology invariant for knots in a rational homology 3 sphere, Topology 33, No. 1, 123-158 (1994)]. In this paper the author gives a method of computing these invariants in the case of fibered knots. It turns out that the invariant is (in special cases) a Lefschetz fixed point number and the method of computation (gauge theory) shows that the invariants of a fibered knot are determined by the Alexander polynomial of the knot.