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math.DG2023
Lie groupoids determined by their orbit spaces
David Miyamoto
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 groupoid…
math.DG2023
Riemannian foliations and quasifolds
Yi Lin, David Miyamoto
It is well known that, by the Reeb stability theorem, the leaf space of a Riemannian foliation with compact leaves is an orbifold. We prove that, under mild completeness conditions…
math.DG2023
Singular foliations through diffeology
David Miyamoto
A singular foliation is a partition of a manifold into leaves of perhaps varying dimension. Stefan and Sussmann carried out fundamental work on singular foliations in the 1970s. We…