Isometric actions on locally compact finite rank median spaces

Mohamed Lamine Messaci

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arXiv · 2309.10760

Isometric actions on locally compact finite rank median spaces

Mohamed Lamine Messaci

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Abstract

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.

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Mohamed Lamine Messaci. 2023-09-19. Isometric actions on locally compact finite rank median spaces. https://arxiv.org/abs/2309.10760

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