Metabelian SL(n,C) representations of knot groups II: fixed points

Hans Boden, Stefan Friedl

Published 2009-09-20, updated 2012-05-25Version 3

Given a knot K in an integral homology sphere with exterior N_K, there is a natural action of the cyclic group Z/n on the space of SL(n,C) representations of the knot group \pi_1(N_K), and this induces an action on the SL(n,C) character variety. We identify the fixed points of this action in terms of characters of metabelian representations, and we apply this to show that the twisted Alexander polynomial associated to an irreducible metabelian SL(n,C) representation is actually a polynomial in t^n.