%0 Journal Article
%T Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$
%A Michael Heusener
%A Ouardia Medjerab
%J Mathematics
%D 2014
%I arXiv
%X Let $K$ be a knot in $S^3$ and $X$ its complement. We study deformations of non-abelian, metabelian, reducible representations of the knot group $\pi\_1(X)$ into $\mathrm{SL}(n,\mathbf{C})$ which are associated to a simple root of the Alexander polynomial. We prove that certain of these metabelian reducible representations are smooth points of the $\mathrm{SL}(n,\mathbf{C})$-representation variety and that they have irreducible deformations.
%U http://arxiv.org/abs/1402.4294v2