Dynamics of Aut(Fn) Actions on Group Presentations and Representations

2011/09/01 by Lubotzky, Alexander · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1109.0155

Abstract

Several different areas of group theory, topology and geometry have led to the study of the action of Aut(Fn) | the automorphism group of the free group on n generators | on Hom(Fn;G) when G is either finite,compact or simple Lie group. In this survey, we describe these topics and results, with special emphasis on some similarities and with an effort to give a somewhat uniform treatment. This perspective sometimes suggests new questions, conjectures and methods borrowed from one area to another.

Cited by

• On Wiegold's conjecture for the small Ree groups
• The Yang-Baxter Equation and Characteristic Finite Simple Quotients of the Free Group of Rank 2

Related

• A presentation for Aut(F_n)
• Aut(Fn) actions on representation spaces
• Short Presentations for Aut_n⁺ and Out_n⁺
• Complexes with free actions by the group of automorphisms of a free group
• Generalized presentations of infinite groups, in particular of Aut(F_ω)