Aut(Fn) actions on representation spaces

TL;DR

This paper explores the actions of automorphism groups on representation spaces for various types of simple groups, extending conjectures from finite simple groups to Lie and algebraic groups.

Contribution

It generalizes Wiegold's conjecture from finite simple groups to compact Lie, non-compact simple analytic, and simple algebraic groups.

Findings

Aut(F_n) acts transitively on Epi(F_n,G) for certain groups G

Extends conjecture to broader classes of groups beyond finite simple groups

Provides new insights into the structure of representation spaces for simple groups

Abstract

J. Wiegold conjectured that if n>2 and G is a finite simple group, then the action of Aut(F_n) on Epi(F_n,G) is transitive. In this note we consider analogous questions where G is a compact Lie group, a non-compact simple analytic group or a simple algebraic group.