Hyperfiniteness for group actions on trees
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912472337743872 |
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| author | Elayavalli, Srivatsav Kunnawalkam Oyakawa, Koichi Shinko, Forte Spaas, Pieter |
| author_facet | Elayavalli, Srivatsav Kunnawalkam Oyakawa, Koichi Shinko, Forte Spaas, Pieter |
| contents | We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfinitenss of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10964 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperfiniteness for group actions on trees Elayavalli, Srivatsav Kunnawalkam Oyakawa, Koichi Shinko, Forte Spaas, Pieter Group Theory Logic Operator Algebras We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfinitenss of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite. |
| title | Hyperfiniteness for group actions on trees |
| topic | Group Theory Logic Operator Algebras |
| url | https://arxiv.org/abs/2307.10964 |