Partial Groupoid Actions on Smooth Manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917880244731904 |
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| author | Marín, Víctor Pinedo, Héctor Rodríguez, J. L. V. |
| author_facet | Marín, Víctor Pinedo, Héctor Rodríguez, J. L. V. |
| contents | Given a smooth partial action $α$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $α$ to be globalizable with smooth globalization. As an application, we provide results on the differentiable structure of orbit and stabilizer spaces induced by $α,$ which leads to other criteria for its globalization in terms of its orbit maps in the case that $α$ is free and transitive. Further, under the assumption that $α$ is free and proper, we prove that there exists exactly one differentiable structure on the quotient structure of the orbit equivalence space $M/G$ such that the quotient map $π:M\to M/G$ is a submersion |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18024 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partial Groupoid Actions on Smooth Manifolds Marín, Víctor Pinedo, Héctor Rodríguez, J. L. V. Differential Geometry Given a smooth partial action $α$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $α$ to be globalizable with smooth globalization. As an application, we provide results on the differentiable structure of orbit and stabilizer spaces induced by $α,$ which leads to other criteria for its globalization in terms of its orbit maps in the case that $α$ is free and transitive. Further, under the assumption that $α$ is free and proper, we prove that there exists exactly one differentiable structure on the quotient structure of the orbit equivalence space $M/G$ such that the quotient map $π:M\to M/G$ is a submersion |
| title | Partial Groupoid Actions on Smooth Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2311.18024 |