Moduli spaces of compact RCD(0,N)-structures
The goal of the paper is to set the foundations and prove some topological results about moduli spaces of non-smooth metric measure structures with non-negative Ricci curvature in a synthetic sense (via optimal transport) on a compact topological space; more precisely, we study moduli spaces of RCD(...
| Главные авторы: | , |
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| Формат: | Journal article |
| Язык: | English |
| Опубликовано: |
Springer
2022
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| _version_ | 1826311596667830272 |
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| author | Mondino, A Navarro, D |
| author_facet | Mondino, A Navarro, D |
| author_sort | Mondino, A |
| collection | OXFORD |
| description | The goal of the paper is to set the foundations and prove some topological results about moduli spaces of non-smooth metric measure structures with non-negative Ricci curvature in a synthetic sense (via optimal transport) on a compact topological space; more precisely, we study moduli spaces of RCD(0,N)-structures. First, we relate the convergence of RCD(0,N)-structures on a space to the associated lifts’ equivariant convergence on the universal cover. Then we construct the Albanese and soul maps, which reflect how structures on the universal cover split, and we prove their continuity. Finally, we construct examples of moduli spaces of RCD(0,N)-structures that have non-trivial rational homotopy groups. |
| first_indexed | 2024-03-07T08:12:06Z |
| format | Journal article |
| id | oxford-uuid:13422d27-a2a6-4355-8ccc-1cbd7cb27040 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:12:06Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:13422d27-a2a6-4355-8ccc-1cbd7cb270402023-12-08T10:09:47ZModuli spaces of compact RCD(0,N)-structuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:13422d27-a2a6-4355-8ccc-1cbd7cb27040EnglishSymplectic ElementsSpringer2022Mondino, ANavarro, DThe goal of the paper is to set the foundations and prove some topological results about moduli spaces of non-smooth metric measure structures with non-negative Ricci curvature in a synthetic sense (via optimal transport) on a compact topological space; more precisely, we study moduli spaces of RCD(0,N)-structures. First, we relate the convergence of RCD(0,N)-structures on a space to the associated lifts’ equivariant convergence on the universal cover. Then we construct the Albanese and soul maps, which reflect how structures on the universal cover split, and we prove their continuity. Finally, we construct examples of moduli spaces of RCD(0,N)-structures that have non-trivial rational homotopy groups. |
| spellingShingle | Mondino, A Navarro, D Moduli spaces of compact RCD(0,N)-structures |
| title | Moduli spaces of compact RCD(0,N)-structures |
| title_full | Moduli spaces of compact RCD(0,N)-structures |
| title_fullStr | Moduli spaces of compact RCD(0,N)-structures |
| title_full_unstemmed | Moduli spaces of compact RCD(0,N)-structures |
| title_short | Moduli spaces of compact RCD(0,N)-structures |
| title_sort | moduli spaces of compact rcd 0 n structures |
| work_keys_str_mv | AT mondinoa modulispacesofcompactrcd0nstructures AT navarrod modulispacesofcompactrcd0nstructures |