Long thin covers and nuclear dimension
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917606990020608 |
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| author | Hirshberg, Ilan Wu, Jianchao |
| author_facet | Hirshberg, Ilan Wu, Jianchao |
| contents | We establish finite nuclear dimension for crossed product C*-algebras arising from various classes of possibly non-free topological actions, including arbitrary actions of finitely generated virtually nilpotent groups on finite dimensional spaces, certain amenable actions of hyperbolic groups, and certain allosteric actions of wreath products. We obtain these results by introducing a new notion of dimension for topological dynamical systems, called the long thin covering dimension, which involves a suitable version of Rokhlin-type towers with controlled overlaps for possibly non-free actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12504 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long thin covers and nuclear dimension Hirshberg, Ilan Wu, Jianchao Operator Algebras Dynamical Systems 46L55 (Primary) 37A55, 46L35 (Secondary) We establish finite nuclear dimension for crossed product C*-algebras arising from various classes of possibly non-free topological actions, including arbitrary actions of finitely generated virtually nilpotent groups on finite dimensional spaces, certain amenable actions of hyperbolic groups, and certain allosteric actions of wreath products. We obtain these results by introducing a new notion of dimension for topological dynamical systems, called the long thin covering dimension, which involves a suitable version of Rokhlin-type towers with controlled overlaps for possibly non-free actions. |
| title | Long thin covers and nuclear dimension |
| topic | Operator Algebras Dynamical Systems 46L55 (Primary) 37A55, 46L35 (Secondary) |
| url | https://arxiv.org/abs/2308.12504 |