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

Abstract

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.

Accepted in Journal of Knot Theory and Its Ramifications