Geometry of the SL(3,C)-character variety of torus knots

Abstract

Let G be the fundamental group of the complement of the torus knot of type (m,n). This has a presentation G=<x,y|x^m=y^n>. We find the geometric description of the character variety X(G) of characters of representations of G into SL(3,C), GL(3,C) and PGL(3,C).

22 pages, no figures. v2. Corrected polynomial in theorem 8.3

References in corpus (2)

• Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups
• Representations of knot groups into ${\mathrm{SL}}_n(\mathbf{C})$ and twisted Alexander polynomials

Cited by in corpus (10)

• Arithmetic of singular character varieties and their $E$-polynomials
• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
• Motive of the $S{L}_4$-character variety of torus knots
• Geometry of $\mathrm{SU}(3)$-character varieties of torus knots
• Representation varieties of twisted Hopf links
• Character Varieties of Generalized Torus Knot Groups
• On high-dimensional representations of knot groups
• On SL(3,$\mathbb{C}$)-representations of the Whitehead link group
• $\mathrm{SL}(3,\mathbb{C})$-character varieties of two-generator groups
• Augmentations and link group representations