Random covers of surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908679801929728 |
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| author | Wright, Sophie |
| author_facet | Wright, Sophie |
| contents | We study random covers of a closed hyperbolic surface $Σ$, subject to the condition that, for $k\geq 2$, the fundamental group is isomorphic to the free group $F_k$. We show that asymptotically they distribute according to a specific probability measure on the moduli space of metric graphs. As we will demonstrate with explicit calculations for $k=2$, this allows us to determine asymptotic values for the expectation of the systole and other geometric invariants of the covers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random covers of surfaces Wright, Sophie Geometric Topology We study random covers of a closed hyperbolic surface $Σ$, subject to the condition that, for $k\geq 2$, the fundamental group is isomorphic to the free group $F_k$. We show that asymptotically they distribute according to a specific probability measure on the moduli space of metric graphs. As we will demonstrate with explicit calculations for $k=2$, this allows us to determine asymptotic values for the expectation of the systole and other geometric invariants of the covers. |
| title | Random covers of surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2511.22731 |