Riemannian foliations and quasifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916374303997952 |
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| author | Lin, Yi Miyamoto, David |
| author_facet | Lin, Yi Miyamoto, David |
| contents | It is well known that, by the Reeb stability theorem, the leaf space of a Riemannian foliation with compact leaves is an orbifold. We prove that, under mild completeness conditions, the leaf space of a Killing Riemannian foliation is a diffeological quasifold: as a diffeological space, it is locally modelled by quotients of Cartesian space by countable groups acting affinely. Furthermore, we prove that the holonomy groupoid of the foliation is, locally, Morita equivalent to the action groupoid of a countable group acting affinely on Cartesian space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15166 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Riemannian foliations and quasifolds Lin, Yi Miyamoto, David Differential Geometry Primary 57S25, Secondary 57R91 It is well known that, by the Reeb stability theorem, the leaf space of a Riemannian foliation with compact leaves is an orbifold. We prove that, under mild completeness conditions, the leaf space of a Killing Riemannian foliation is a diffeological quasifold: as a diffeological space, it is locally modelled by quotients of Cartesian space by countable groups acting affinely. Furthermore, we prove that the holonomy groupoid of the foliation is, locally, Morita equivalent to the action groupoid of a countable group acting affinely on Cartesian space. |
| title | Riemannian foliations and quasifolds |
| topic | Differential Geometry Primary 57S25, Secondary 57R91 |
| url | https://arxiv.org/abs/2309.15166 |