Subexponential growth and $C^1$ actions on one-manifolds
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909334680633344 |
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| author | Kim, Sang-hyun Bon, Nicolás Matte de la Salle, Mikael Triestino, Michele |
| author_facet | Kim, Sang-hyun Bon, Nicolás Matte de la Salle, Mikael Triestino, Michele |
| contents | Let $G$ be a countable group with no finitely generated subgroup of exponential growth. We show that every action of $G$ on a countable set preserving a linear (respectively, circular) order can be realised as the restriction of some action by $C^1$ diffeomorphisms on an interval (respectively, the circle) to an invariant subset. As a consequence, every action of $G$ by homeomorphisms on a compact connected one-manifold can be made $C^1$ upon passing to a semi-conjugate action. The proof is based on a functional characterisation of groups of local subexponential growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subexponential growth and $C^1$ actions on one-manifolds Kim, Sang-hyun Bon, Nicolás Matte de la Salle, Mikael Triestino, Michele Group Theory Dynamical Systems Let $G$ be a countable group with no finitely generated subgroup of exponential growth. We show that every action of $G$ on a countable set preserving a linear (respectively, circular) order can be realised as the restriction of some action by $C^1$ diffeomorphisms on an interval (respectively, the circle) to an invariant subset. As a consequence, every action of $G$ by homeomorphisms on a compact connected one-manifold can be made $C^1$ upon passing to a semi-conjugate action. The proof is based on a functional characterisation of groups of local subexponential growth. |
| title | Subexponential growth and $C^1$ actions on one-manifolds |
| topic | Group Theory Dynamical Systems |
| url | https://arxiv.org/abs/2410.02614 |