Invariant random subgroups in hyperbolic reflection groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917184830177280 |
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| author | Raimbault, Jean |
| author_facet | Raimbault, Jean |
| contents | We prove that the Fuchsian (4,4,4) triangle group and also right-angled reflection groups of hyperbolic spaces in higher dimensions admit ergodic invariant random subgroups having uncountably many isomorphism types of subgroups in their support (in most cases we actually prove a stronger statement), providing an answer to a question of S. Thomas. We also give similar constructions in higher-dimensional spaces. Our constructions are based on Coxeter polytopes in hyperbolic spaces. We also provide examples of invariant random subgroups related to questions of Y. Glasner and A. Hase through a similar construction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_02195 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant random subgroups in hyperbolic reflection groups Raimbault, Jean Group Theory We prove that the Fuchsian (4,4,4) triangle group and also right-angled reflection groups of hyperbolic spaces in higher dimensions admit ergodic invariant random subgroups having uncountably many isomorphism types of subgroups in their support (in most cases we actually prove a stronger statement), providing an answer to a question of S. Thomas. We also give similar constructions in higher-dimensional spaces. Our constructions are based on Coxeter polytopes in hyperbolic spaces. We also provide examples of invariant random subgroups related to questions of Y. Glasner and A. Hase through a similar construction. |
| title | Invariant random subgroups in hyperbolic reflection groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2601.02195 |