Lie groupoids determined by their orbit spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929286329401344 |
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| author | Miyamoto, David |
| author_facet | Miyamoto, David |
| contents | Given a Lie groupoid, we can form its orbit space, which carries a natural diffeology. More generally, we have a quotient functor from the Hilsum-Skandalis category of Lie groupoids to the category of diffeological spaces. We introduce the notion of a lift-complete Lie groupoid, and show that the quotient functor restricts to an equivalence of the categories: of lift-complete Lie groupoids with isomorphism classes of surjective submersive bibundles as arrows, and of quasi-étale diffeological spaces with surjective local subductions as arrows. In particular, the Morita equivalence class of a lift-complete Lie groupoid, alternatively a lift-complete differentiable stack, is determined by its diffeological orbit space. Examples of lift-complete Lie groupoids include quasifold groupoids and étale holonomy groupoids of Riemannian foliations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11968 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lie groupoids determined by their orbit spaces Miyamoto, David Differential Geometry 58H05, 57R30, 57P05 Given a Lie groupoid, we can form its orbit space, which carries a natural diffeology. More generally, we have a quotient functor from the Hilsum-Skandalis category of Lie groupoids to the category of diffeological spaces. We introduce the notion of a lift-complete Lie groupoid, and show that the quotient functor restricts to an equivalence of the categories: of lift-complete Lie groupoids with isomorphism classes of surjective submersive bibundles as arrows, and of quasi-étale diffeological spaces with surjective local subductions as arrows. In particular, the Morita equivalence class of a lift-complete Lie groupoid, alternatively a lift-complete differentiable stack, is determined by its diffeological orbit space. Examples of lift-complete Lie groupoids include quasifold groupoids and étale holonomy groupoids of Riemannian foliations. |
| title | Lie groupoids determined by their orbit spaces |
| topic | Differential Geometry 58H05, 57R30, 57P05 |
| url | https://arxiv.org/abs/2310.11968 |