Rigidity of the dynamics of ${\rm Aut}({\mathsf{F}}_n)$ on representations into a compact group
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917328410640384 |
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| author | Cantat, Serge Dupont, Christophe Martin-Baillon, Florestan |
| author_facet | Cantat, Serge Dupont, Christophe Martin-Baillon, Florestan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09456 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity of the dynamics of ${\rm Aut}({\mathsf{F}}_n)$ on representations into a compact group Cantat, Serge Dupont, Christophe Martin-Baillon, Florestan Dynamical Systems Group Theory 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. |
| title | Rigidity of the dynamics of ${\rm Aut}({\mathsf{F}}_n)$ on representations into a compact group |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2603.09456 |