English

Rigidity of the dynamics of ${{\rm Aut}}({\mathsf{F}}_n)$ on representations into a compact group

Dynamical Systems 2026-03-11 v1 Group Theory

Abstract

Let GG be a compact Lie group. Let Fn{\mathsf{F}}_n be the free group of rank nn. We describe the orbits of Aut(Fn){\mathsf{Aut}}(\mathsf{F}_n) on Hom(Fn;G){\mathsf{Hom}}(\mathsf{F}_n;G) when nn is sufficiently large. The dynamics stabilizes: orbit closures and invariant probability measures are algebraic, as in Ratner's theorems.

Keywords

Cite

@article{arxiv.2603.09456,
  title  = {Rigidity of the dynamics of ${{\rm Aut}}({\mathsf{F}}_n)$ on representations into a compact group},
  author = {Serge Cantat and Christophe Dupont and Florestan Martin-Baillon},
  journal= {arXiv preprint arXiv:2603.09456},
  year   = {2026}
}