The Space of Actions, Partition Metric and Combinatorial Rigidity
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2011
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| _version_ | 1866909537807630336 |
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| author | Abert, Miklos Elek, Gabor |
| author_facet | Abert, Miklos Elek, Gabor |
| contents | We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kechris, and the metric identification is compact. We achieve this by employing symbolic dynamics and an ultraproduct construction which also facilitates the extension of our results to unitary representations. As a byproduct, we show that the weak equivalence class of every free non-amenable action contains an action that satisfies the measurable von Neumann problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1108_2147 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | The Space of Actions, Partition Metric and Combinatorial Rigidity Abert, Miklos Elek, Gabor Functional Analysis Group Theory 37A15 We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kechris, and the metric identification is compact. We achieve this by employing symbolic dynamics and an ultraproduct construction which also facilitates the extension of our results to unitary representations. As a byproduct, we show that the weak equivalence class of every free non-amenable action contains an action that satisfies the measurable von Neumann problem. |
| title | The Space of Actions, Partition Metric and Combinatorial Rigidity |
| topic | Functional Analysis Group Theory 37A15 |
| url | https://arxiv.org/abs/1108.2147 |