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arXiv · 2603.09456

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

Serge Cantat·Christophe Dupont·Florestan Martin-Baillon
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Abstract

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

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Serge Cantat, Christophe Dupont, Florestan Martin-Baillon. 2026-03-10. Rigidity of the dynamics of ${{\rm Aut}}({\mathsf{F}}_n)$ on representations into a compact group. https://arxiv.org/abs/2603.09456

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