Year: 2025
Type: article
Abstract: Given a smooth partial action $$\alpha $$ α of a Lie groupoid G on a smooth manifold M, we provide necessary and sufficient conditions for $$\alpha $$ α to be globalizable with smooth globalization. As an application, we provide results on the differentiable structure of orbit and stabilizer spaces induced by $$\alpha ,$$ α , which leads to other criteria for its globalization in terms of its orbit maps in the case that $$\alpha $$ α is free and transitive. Further, under the assumption that $$\alpha $$ 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 $$\pi :M\rightarrow M/G$$ π : M → M / G is a submersion.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4407681112