Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$

Michael Heusener (1) , Ouardia Medjerab (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 ENS Kouba-Alger - École normale supérieure - Kouba-Alger

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.

Mots clés: Representations of knot groups; $\mathrm{SL}(n; \mathbf{C})$-representation variety; metabelian representations

Domaines: Topologie géométrique [math.GT]

Michael Heusener, Ouardia Medjerab. Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$. 2014. ⟨hal-00948334v1⟩