Obstructions for quantitative measure equivalence between locally compact groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908968931033088 |
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| author | Correia, Corentin Paucar, Juan |
| author_facet | Correia, Corentin Paucar, Juan |
| contents | Given a measure equivalence coupling between two finitely generated groups, Delabie, Koivisto, Le Maître and Tessera have found explicit upper bounds on how integrable the associated cocycles can be. We extend these results to the broader framework of unimodular compactly generated locally compact groups. We also generalize a result by the first-named author, showing that the integrability threshold described in these statements cannot be achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Obstructions for quantitative measure equivalence between locally compact groups Correia, Corentin Paucar, Juan Group Theory Dynamical Systems 37A20, 22D05, 22F10, 22D40, 20F69, 20F65 Given a measure equivalence coupling between two finitely generated groups, Delabie, Koivisto, Le Maître and Tessera have found explicit upper bounds on how integrable the associated cocycles can be. We extend these results to the broader framework of unimodular compactly generated locally compact groups. We also generalize a result by the first-named author, showing that the integrability threshold described in these statements cannot be achieved. |
| title | Obstructions for quantitative measure equivalence between locally compact groups |
| topic | Group Theory Dynamical Systems 37A20, 22D05, 22F10, 22D40, 20F69, 20F65 |
| url | https://arxiv.org/abs/2510.25321 |