Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$

Leila Ben Abdelghani, Michael Heusener, Hajer Jebali

Published 2007-10-18, updated 2008-10-16Version 3

Let K be a knot in $S^3$ and $X$ its complement. We study deformations of reducible metabelian representations of the knot group $\pi_1(X)$ into $SL(3,\mathbb{C})$ which are associated to a double root of the Alexander polynomial. We prove that these reducible metabelian representations are smooth points of the representation variety and that they have irreducible non metabelian deformations.