The systole of random hyperbolic 3-manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866911920914694144 |
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| author | Roig-Sanchis, Anna |
| author_facet | Roig-Sanchis, Anna |
| contents | We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault, answering a question posed in that same article. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that the limit, as the volume tends to infinity, of the expected value of their systole exists and we give a closed formula of it. Moreover, we compute a numerical approximation of this value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The systole of random hyperbolic 3-manifolds Roig-Sanchis, Anna Geometric Topology Differential Geometry Probability 57K32, 57K31, 60C05 We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault, answering a question posed in that same article. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that the limit, as the volume tends to infinity, of the expected value of their systole exists and we give a closed formula of it. Moreover, we compute a numerical approximation of this value. |
| title | The systole of random hyperbolic 3-manifolds |
| topic | Geometric Topology Differential Geometry Probability 57K32, 57K31, 60C05 |
| url | https://arxiv.org/abs/2406.11783 |