Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916991427674112 |
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| author | Peng, Bo |
| author_facet | Peng, Bo |
| contents | We show that the isomorphism of ergodic measure-preserving transformations is not Borel reducible to the relation induced by the conjugacy action of the full group of an ergodic measure-preserving transformation on itself. This answers a question of Le Maître in the negative and gives a positive indication towards a conjecture of Sabok. In fact, we prove that the isomorphism of ergodic measure-preserving transformation is unbalanced, which answers another question of Le Maître in the positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations Peng, Bo Dynamical Systems Logic 37A35 We show that the isomorphism of ergodic measure-preserving transformations is not Borel reducible to the relation induced by the conjugacy action of the full group of an ergodic measure-preserving transformation on itself. This answers a question of Le Maître in the negative and gives a positive indication towards a conjecture of Sabok. In fact, we prove that the isomorphism of ergodic measure-preserving transformation is unbalanced, which answers another question of Le Maître in the positive. |
| title | Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations |
| topic | Dynamical Systems Logic 37A35 |
| url | https://arxiv.org/abs/2510.04989 |