Geometric property (T) for box spaces and sofic approximations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918211877863424 |
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| author | Alekseev, Vadim Drigalla, Stefan |
| author_facet | Alekseev, Vadim Drigalla, Stefan |
| contents | We prove that every sofic approximation of a property (T) group is approximately isomorphic to one having geometric property (T), and more generally, a box space of graphs which has boundary geometric property (T) is approximately isomorphic to one having geometric property (T). We also prove that a sequence of bounded degree graphs is approximately isomorphic to a disjoint union of expanders if and only if the Laplacian has spectral gap in the ultraproduct. Finally, we prove a local geometric criterion for geometric property (T) in the spirit of Żuk's criterion for property (T) for groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric property (T) for box spaces and sofic approximations Alekseev, Vadim Drigalla, Stefan Group Theory Metric Geometry Operator Algebras 20F65, 51F30, 05C25, 20L05, 46L55 We prove that every sofic approximation of a property (T) group is approximately isomorphic to one having geometric property (T), and more generally, a box space of graphs which has boundary geometric property (T) is approximately isomorphic to one having geometric property (T). We also prove that a sequence of bounded degree graphs is approximately isomorphic to a disjoint union of expanders if and only if the Laplacian has spectral gap in the ultraproduct. Finally, we prove a local geometric criterion for geometric property (T) in the spirit of Żuk's criterion for property (T) for groups. |
| title | Geometric property (T) for box spaces and sofic approximations |
| topic | Group Theory Metric Geometry Operator Algebras 20F65, 51F30, 05C25, 20L05, 46L55 |
| url | https://arxiv.org/abs/2511.16515 |