Non-Hausdorff germinal groupoids for actions of countable groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909222682230784 |
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| author | Lukina, Olga |
| author_facet | Lukina, Olga |
| contents | We study conditions under which the germinal groupoid associated to a minimal equicontinuous action of a countable group on a Cantor set has non-Hausdorff topology. We develop a new criterion, which serves as an obstruction for the étale topology on the groupoid to be non-Hausdorff. We use this and other criteria to study the topology of germinal groupoids for a few classes of actions. In particular, we give examples of families of contracting and non-contracting self-similar groups, which are amenable and whose actions have associated germinal groupoids with non-Hausdorff topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06340 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Hausdorff germinal groupoids for actions of countable groups Lukina, Olga Dynamical Systems Group Theory Primary: 22A22, 37B05, Secondary: 22C05, 22A05, 37B45 We study conditions under which the germinal groupoid associated to a minimal equicontinuous action of a countable group on a Cantor set has non-Hausdorff topology. We develop a new criterion, which serves as an obstruction for the étale topology on the groupoid to be non-Hausdorff. We use this and other criteria to study the topology of germinal groupoids for a few classes of actions. In particular, we give examples of families of contracting and non-contracting self-similar groups, which are amenable and whose actions have associated germinal groupoids with non-Hausdorff topology. |
| title | Non-Hausdorff germinal groupoids for actions of countable groups |
| topic | Dynamical Systems Group Theory Primary: 22A22, 37B05, Secondary: 22C05, 22A05, 37B45 |
| url | https://arxiv.org/abs/2309.06340 |