Coarsely separation of groups and spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913279589220352 |
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| author | Tselekidis, Panagiotis |
| author_facet | Tselekidis, Panagiotis |
| contents | Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension $n$ containing a bi-infinite geodesic can be coarsely separated by a subset $S$ of asymptotic dimension equal to or smaller than $n-1$.\\ We define asymptotic Cantor manifolds, and we prove that every finitely generated group contains such a manifold. We also state some questions related to them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coarsely separation of groups and spaces Tselekidis, Panagiotis Group Theory Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension $n$ containing a bi-infinite geodesic can be coarsely separated by a subset $S$ of asymptotic dimension equal to or smaller than $n-1$.\\ We define asymptotic Cantor manifolds, and we prove that every finitely generated group contains such a manifold. We also state some questions related to them. |
| title | Coarsely separation of groups and spaces |
| topic | Group Theory |
| url | https://arxiv.org/abs/2403.15892 |