Isometric actions on locally compact finite rank median spaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914704161505280 |
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| author | Messaci, Mohamed Lamine |
| author_facet | Messaci, Mohamed Lamine |
| contents | We prove that a connected locally compact median space of finite rank which admits a transitive action is isometric to $\mathbb{R}^n$ endowed with the $\ell^1$-metric. In the other side, replacing the transitivity assumption on the group of isometries by a certain regularity of the action on the compactification of the space, we show that all orbits are discrete. In our way to prove these results, we give a characterization of the compactness in complete median spaces of finite rank by the combinatorics of their halfspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10760 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isometric actions on locally compact finite rank median spaces Messaci, Mohamed Lamine Geometric Topology Metric Geometry 20F65, 22F50, 51F99 We prove that a connected locally compact median space of finite rank which admits a transitive action is isometric to $\mathbb{R}^n$ endowed with the $\ell^1$-metric. In the other side, replacing the transitivity assumption on the group of isometries by a certain regularity of the action on the compactification of the space, we show that all orbits are discrete. In our way to prove these results, we give a characterization of the compactness in complete median spaces of finite rank by the combinatorics of their halfspaces. |
| title | Isometric actions on locally compact finite rank median spaces |
| topic | Geometric Topology Metric Geometry 20F65, 22F50, 51F99 |
| url | https://arxiv.org/abs/2309.10760 |