Dynamics on the perfect kernel of higher rank generalized Baumslag-Solitar groups
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911185845092352 |
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| author | Bontemps, Sasha |
| author_facet | Bontemps, Sasha |
| contents | In this article, we study the space of subgroups of non-amenable generalized Baumslag-Solitar groups (GBS groups) of rank $d$, that is, groups acting cocompactly on an oriented tree with vertex and edge stabilizers isomorphic to $\mathbb{Z}^d$. Our results generalize the study of Baumslag-Solitar groups, and of GBS groups of rank $1$. We give an explicit description of the perfect kernel of a non-amenable GBS group $G$ of rank $d$ and show the existence of a partition of the perfect kernel into a countably infinite set of pieces which are invariant under the action by conjugation of $G$, and such that each piece contains a dense orbit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics on the perfect kernel of higher rank generalized Baumslag-Solitar groups Bontemps, Sasha Group Theory Dynamical Systems 37B, 20E06, 20E08 In this article, we study the space of subgroups of non-amenable generalized Baumslag-Solitar groups (GBS groups) of rank $d$, that is, groups acting cocompactly on an oriented tree with vertex and edge stabilizers isomorphic to $\mathbb{Z}^d$. Our results generalize the study of Baumslag-Solitar groups, and of GBS groups of rank $1$. We give an explicit description of the perfect kernel of a non-amenable GBS group $G$ of rank $d$ and show the existence of a partition of the perfect kernel into a countably infinite set of pieces which are invariant under the action by conjugation of $G$, and such that each piece contains a dense orbit. |
| title | Dynamics on the perfect kernel of higher rank generalized Baumslag-Solitar groups |
| topic | Group Theory Dynamical Systems 37B, 20E06, 20E08 |
| url | https://arxiv.org/abs/2509.26143 |