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

Abstract

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.

To appear in Mathematica Slovaca

Cited by in corpus (4)

• Representations of knot groups into ${\mathrm{SL}}_n(\mathbf{C})$ and twisted Alexander polynomials
• The SL(3,C)-character variety of the figure eight knot
• Irreducible representations of knot groups into SL(n,C)
• Deformations of reducible SL(n,C) representations of fibered 3-manifold groups