Elementwise conservative actions and new constructions of boomerang subgroups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917167036891136 |
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| author | Glasner, Yair Hartnick, Tobias Lederle, Waltraud |
| author_facet | Glasner, Yair Hartnick, Tobias Lederle, Waltraud |
| contents | We show that countable non-abelian free groups admit uncountably many mutually singular elementwise conservative non-singular random subgroups, which are supported on infinite subgroups of infinite index and singular with respect to every invariant random subgroup. This complements recent rigidity results for elementwise-conservative random subgroups in higher rank lattices by the first- and third-named authors. Our proof is based on a study of representations of free groups into measurable full groups in which the action of the first generator of the free group is fixed. We show that elementwise conservativity is generic among such representations in the sense of Baire category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elementwise conservative actions and new constructions of boomerang subgroups Glasner, Yair Hartnick, Tobias Lederle, Waltraud Group Theory Dynamical Systems 37A40, 37A40, 37A15, 22F10 We show that countable non-abelian free groups admit uncountably many mutually singular elementwise conservative non-singular random subgroups, which are supported on infinite subgroups of infinite index and singular with respect to every invariant random subgroup. This complements recent rigidity results for elementwise-conservative random subgroups in higher rank lattices by the first- and third-named authors. Our proof is based on a study of representations of free groups into measurable full groups in which the action of the first generator of the free group is fixed. We show that elementwise conservativity is generic among such representations in the sense of Baire category. |
| title | Elementwise conservative actions and new constructions of boomerang subgroups |
| topic | Group Theory Dynamical Systems 37A40, 37A40, 37A15, 22F10 |
| url | https://arxiv.org/abs/2512.20596 |