Knot invariants and representation varieties
by
Hans U. Boden
McMaster University

Invariants of fibered knots in a rational homology sphere are defined using SU(n) representations of the knot group. In the case n=2, these specialize to Casson's invariant. These invariants detect irreducible SU(n) representations of the knot groups satisfying a monodromy condition along the longitude. The particular monodromy condition imposed is given by choosing a conjugacy class in the group SU(n), thus we get a family of invariants parametrized by SU(n) modulo conjugation. We study the effect on the invariants of varying the holonomy condition. With respect to a particular chamber structure on the parameter space, the invariants are constant within chambers and change by the product of two lower rank invariants when one moves between adjacent chambers.

Date received: January 26, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-17.