Density of systoles of hyperbolic manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915014612353024 |
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| author | Douba, Sami Huang, Junzhi |
| author_facet | Douba, Sami Huang, Junzhi |
| contents | We show that for each $n \geq 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty)$. We also show that for any $n\geq 2$ and any Salem number $λ$, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log(λ)$. In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density of systoles of hyperbolic manifolds Douba, Sami Huang, Junzhi Geometric Topology Group Theory Number Theory We show that for each $n \geq 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty)$. We also show that for any $n\geq 2$ and any Salem number $λ$, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log(λ)$. In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +\infty)$. |
| title | Density of systoles of hyperbolic manifolds |
| topic | Geometric Topology Group Theory Number Theory |
| url | https://arxiv.org/abs/2404.15927 |