Subgroup mixing in Baumslag-Solitar groups
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908839727595520 |
|---|---|
| author | Bontemps, Sasha |
| author_facet | Bontemps, Sasha |
| contents | In this article, we contribute to the study of the dynamics induced by the conjugation action on the space of subgroups of Baumslag-Solitar groups BS(m,n), via the mixing properties of elements asymptotically produced by suitable random walks on the group. In an acylindrically hyperbolic context, the authors of [HMO] demonstrated strong mixing situations, namely topological mu-mixing, a strengthening of high topological transitivity. Regarding non-metabelian and non-unimodular BS(m,n), we exhibit here a radically different situation on each of the pieces except one of the partition introduced in [CGLMS22] (although it is highly topologically transitive on each piece). On the other hand, when BS(m,n) is unimodular, we demonstrate the topological mu-mixing character on each of the pieces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subgroup mixing in Baumslag-Solitar groups Bontemps, Sasha Group Theory Dynamical Systems Probability 37B, 20E06, 20E08, 60G50 In this article, we contribute to the study of the dynamics induced by the conjugation action on the space of subgroups of Baumslag-Solitar groups BS(m,n), via the mixing properties of elements asymptotically produced by suitable random walks on the group. In an acylindrically hyperbolic context, the authors of [HMO] demonstrated strong mixing situations, namely topological mu-mixing, a strengthening of high topological transitivity. Regarding non-metabelian and non-unimodular BS(m,n), we exhibit here a radically different situation on each of the pieces except one of the partition introduced in [CGLMS22] (although it is highly topologically transitive on each piece). On the other hand, when BS(m,n) is unimodular, we demonstrate the topological mu-mixing character on each of the pieces. |
| title | Subgroup mixing in Baumslag-Solitar groups |
| topic | Group Theory Dynamical Systems Probability 37B, 20E06, 20E08, 60G50 |
| url | https://arxiv.org/abs/2505.07667 |