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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.14944 |
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| _version_ | 1866909915351613440 |
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| author | Bal, Jashan |
| author_facet | Bal, Jashan |
| contents | We study projectivity in the category of $G$-flows and affine $G$-flows for Polish groups $G$. We also introduce the notion of \emph{proximally irreducible} extensions between affine $G$-flows. Using this we provide a characterization of extreme amenability, strong amenability, and amenability for closed subgroups $H \leq G$ in terms of certain ``dynamical irreducibility'' properties of the Samuel compactification of $G/H$. We then apply this to answer an open question of Zucker by proving a structure theorem for when the universal minimal proximal flow of $G$ is metrizable or contains a comeager orbit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projectivity in topological dynamics Bal, Jashan Dynamical Systems Logic 37B05 (Primary) 03E15, 46M10 (Secondary) We study projectivity in the category of $G$-flows and affine $G$-flows for Polish groups $G$. We also introduce the notion of \emph{proximally irreducible} extensions between affine $G$-flows. Using this we provide a characterization of extreme amenability, strong amenability, and amenability for closed subgroups $H \leq G$ in terms of certain ``dynamical irreducibility'' properties of the Samuel compactification of $G/H$. We then apply this to answer an open question of Zucker by proving a structure theorem for when the universal minimal proximal flow of $G$ is metrizable or contains a comeager orbit. |
| title | Projectivity in topological dynamics |
| topic | Dynamical Systems Logic 37B05 (Primary) 03E15, 46M10 (Secondary) |
| url | https://arxiv.org/abs/2511.14944 |