The Moduli Stack of Compact Metric Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910081014038528 |
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| author | Yuji, Tomoki |
| author_facet | Yuji, Tomoki |
| contents | In this paper, we introduce a Grothendieck topology on the category of totally bounded metric spaces and develop a theory of stacks with respect to this topology. We further define the fine moduli stack of compact metric spaces and prove that its coarse moduli space is isometric to the Gromov--Hausdorff space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Moduli Stack of Compact Metric Spaces Yuji, Tomoki Metric Geometry In this paper, we introduce a Grothendieck topology on the category of totally bounded metric spaces and develop a theory of stacks with respect to this topology. We further define the fine moduli stack of compact metric spaces and prove that its coarse moduli space is isometric to the Gromov--Hausdorff space. |
| title | The Moduli Stack of Compact Metric Spaces |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2512.22847 |