Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.14081 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $d$ be a square free positive integer and $\mathbb{Q}(\sqrt{d})$ a totally real quadratic field over $\mathbb{Q}$. We show there exists an arithmetic lattice L in $SL(8,\mathbb{R})$ with entries in the ring of integers of $\mathbb{Q}(\sqrt{d})$ and a sequence of lattices $Γ_n $ commensurable to L such that the systole of the locally symmetric finite volume manifold $Γ_n \diagdown SL(8,\mathbb{R}) \diagup SO(8)$ goes to infinity as $n \rightarrow \infty$, yet every $Γ_n$ contains the same hyperbolic 3-manifold group $Π$, a finite index subgroup of the arithmetic hyperbolic 3-manifold vol3. Notably, such an example does not exist in rank one, so this is a feature unique to higher rank lattices.