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arXiv · 2311.18024

Partial Groupoid Actions on Smooth Manifolds

Víctor Marín·Héctor Pinedo·J. L. V. Rodríguez
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Abstract

Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be globalizable with smooth globalization. As an application, we provide results on the differentiable structure of orbit and stabilizer spaces induced by $\alpha,$ which leads to other criteria for its globalization in terms of its orbit maps in the case that $\alpha$ is free and transitive. Further, under the assumption that $\alpha$ 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 $\pi:M\to M/G$ is a submersion

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Víctor Marín, Héctor Pinedo, J. L. V. Rodríguez. 2023-11-29. Partial Groupoid Actions on Smooth Manifolds. https://arxiv.org/abs/2311.18024

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