Varieties of Characters

Abstract

Let G be a connected reductive affine algebraic group. In this short note we define the "variety of G-characters" of a finitely generated group F and show that the quotient of the G-character variety of F by the action of the trace preserving outer automorphisms of G normalizes the variety of G-characters when F is a free group, free abelian group, or a surface group.

12 pages, this version fixes a small error in the published version

References in corpus (3)

• Exceptional Lie groups
• Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups
• Homotopy Groups of Free Group Character Varieties

Cited by in corpus (8)

• Rank 1 character varieties of finitely presented groups
• Motive of the $S{L}_4$-character variety of torus knots
• Representation variety for the rank one affine group
• Representation varieties of twisted Hopf links
• When does the zero fiber of the moment map have rational singularities?
• Bad Representations and Homotopy of Character Varieties
• Non-strict plurisubharmonicity of energy on Teichmüller space
• Dynamics on the SU(2,1)-character variety of the one-holed torus