Deformations of dihedral representations

Abstract

ABiSTRACT. G. Burde proved (1990) that the SU2(C) representation space of two-bridge knot groups is one-dimensional. 'T'he same holds for all torus knot groups. 'T'he aim of this note is to prove the following: Given a knot k C S3 we denote by 02 its twofold branched covering space. Assume that there is a prime number p such that HI (02, p) Zp. 'T'hen there exist representations of the knot group onto the binary dihedral group Dp c SU2 (C) and these representations are smooth points on a one-dimensional curve of representations into SU2(C).