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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.03535 |
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| _version_ | 1866908301534429184 |
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| author | Derimay, Antoine |
| author_facet | Derimay, Antoine |
| contents | We introduce a new Polish group, called the commensurating full group, associated to an ergodic measure-class preserving transformation of a standard atomless probability space. It is an analogue of the $\rm L^1$ full group defined by Le Maître, which does not need the transformation to preserve a measure to be defined. We prove, among others, that it is a complete invariant of flip conjugacy, and that it is quasi-isometric to the line in the sense of Rosendal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the commensurating full group Derimay, Antoine Dynamical Systems Group Theory We introduce a new Polish group, called the commensurating full group, associated to an ergodic measure-class preserving transformation of a standard atomless probability space. It is an analogue of the $\rm L^1$ full group defined by Le Maître, which does not need the transformation to preserve a measure to be defined. We prove, among others, that it is a complete invariant of flip conjugacy, and that it is quasi-isometric to the line in the sense of Rosendal. |
| title | On the commensurating full group |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2504.03535 |