Moduli spaces of flat Riemannian metrics on orbifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911069260218368 |
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| author | García, Karla Solis, Ingrid Amaranta Membrillo Valiunas, Motiejus |
| author_facet | García, Karla Solis, Ingrid Amaranta Membrillo Valiunas, Motiejus |
| contents | We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds $\mathcal{O}$, the Teichmüller space of flat metrics $\mathcal{T}_{\text{flat}}(\mathcal{O})$ serves as a classifying space for proper actions of the mapping class group, $\operatorname{MCG}(\mathcal{O})$, in the appropriate category. We show that the moduli space of flat metrics, $\mathcal{M}_{\text{flat}}(\mathcal{O}) = \mathcal{T}_{\text{flat}}(\mathcal{O}) / \operatorname{MCG}(\mathcal{O})$, is itself a very good orbifold, and, under a technical assumption, describe this orbifold algebraically up to commensurability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli spaces of flat Riemannian metrics on orbifolds García, Karla Solis, Ingrid Amaranta Membrillo Valiunas, Motiejus Differential Geometry Group Theory Geometric Topology 57R18 (primary), 20H15, 57S05 (secondary) We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds $\mathcal{O}$, the Teichmüller space of flat metrics $\mathcal{T}_{\text{flat}}(\mathcal{O})$ serves as a classifying space for proper actions of the mapping class group, $\operatorname{MCG}(\mathcal{O})$, in the appropriate category. We show that the moduli space of flat metrics, $\mathcal{M}_{\text{flat}}(\mathcal{O}) = \mathcal{T}_{\text{flat}}(\mathcal{O}) / \operatorname{MCG}(\mathcal{O})$, is itself a very good orbifold, and, under a technical assumption, describe this orbifold algebraically up to commensurability. |
| title | Moduli spaces of flat Riemannian metrics on orbifolds |
| topic | Differential Geometry Group Theory Geometric Topology 57R18 (primary), 20H15, 57S05 (secondary) |
| url | https://arxiv.org/abs/2507.16017 |