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Partial Groupoid Actions on Smooth Manifolds
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Journal Article
Partial Groupoid Actions on Smooth Manifolds
2025
Overview
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
→
M
/
G
is a submersion.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
