Convex cores for actions on finite-rank median algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912979251888128 |
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| author | Fioravanti, Elia |
| author_facet | Fioravanti, Elia |
| contents | We show that every action of a finitely generated group on a finite-rank median algebra admits a nonempty "convex core", even when no metric or topology is given. We then use this to deduce an analogue of the flat torus theorem for actions on connected finite-rank median spaces. We also prove that isometries of connected finite-rank median spaces are either elliptic or loxodromic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_03060 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Convex cores for actions on finite-rank median algebras Fioravanti, Elia Geometric Topology Group Theory We show that every action of a finitely generated group on a finite-rank median algebra admits a nonempty "convex core", even when no metric or topology is given. We then use this to deduce an analogue of the flat torus theorem for actions on connected finite-rank median spaces. We also prove that isometries of connected finite-rank median spaces are either elliptic or loxodromic. |
| title | Convex cores for actions on finite-rank median algebras |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2101.03060 |