Remarks on discrete subgroups with full limit sets in higher rank Lie groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912549997379584 |
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| author | Dey, Subhadip Hurtado, Sebastian |
| author_facet | Dey, Subhadip Hurtado, Sebastian |
| contents | We show that real semi-simple Lie groups of higher rank contain (infinitely generated) discrete subgroups with full limit sets in the corresponding Furstenberg boundaries. Additionally, we provide criteria under which discrete subgroups of $G = \operatorname{SL}(3,\mathbb{R})$ must have a full limit set in the Furstenberg boundary of $G$.
In the appendix, we show the the existence of Zariski-dense discrete subgroups $Γ$ of $\operatorname{SL}(n,\mathbb{R})$, where $n\ge 3$, such that the Jordan projection of some loxodromic element $γ\inΓ$ lies on the boundary of the limit cone of $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on discrete subgroups with full limit sets in higher rank Lie groups Dey, Subhadip Hurtado, Sebastian Geometric Topology Dynamical Systems Group Theory 22E40, 53C35, 14M15 We show that real semi-simple Lie groups of higher rank contain (infinitely generated) discrete subgroups with full limit sets in the corresponding Furstenberg boundaries. Additionally, we provide criteria under which discrete subgroups of $G = \operatorname{SL}(3,\mathbb{R})$ must have a full limit set in the Furstenberg boundary of $G$. In the appendix, we show the the existence of Zariski-dense discrete subgroups $Γ$ of $\operatorname{SL}(n,\mathbb{R})$, where $n\ge 3$, such that the Jordan projection of some loxodromic element $γ\inΓ$ lies on the boundary of the limit cone of $Γ$. |
| title | Remarks on discrete subgroups with full limit sets in higher rank Lie groups |
| topic | Geometric Topology Dynamical Systems Group Theory 22E40, 53C35, 14M15 |
| url | https://arxiv.org/abs/2405.10209 |