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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2403.14081 |
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| _version_ | 1866909800329117696 |
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| author | Hillen, Paige |
| author_facet | Hillen, Paige |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Uniform Lattices of Large Systole Containing a Fixed 3-Manifold Group Hillen, Paige Geometric Topology 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. |
| title | Non-Uniform Lattices of Large Systole Containing a Fixed 3-Manifold Group |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2403.14081 |