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Diffeological approaches to leaf spaces of foliations

Posted in
David Miyamoto
Mit, 11/10/2023 - 11:00 - 12:30
MPIM Seminar Room

A singular foliation $\mathcal{F}$ partitions a manifold $M$ into leaves. The leaf space $M/\mathcal{F}$ is often quite singular, but still carries a natural quotient diffeology. We take three approaches to the question: what data in $\mathcal{F}$ is preserved in $M/\mathcal{F}$? First, we give sufficient conditions for the preservation of the basic cohomology. Second, we show that regular Riemannian foliations are determined, up to transverse equivalence, by their leaf spaces. Finally, we define a transverse equivalence of singular foliations (Molino transverse equivalence), and show this induces a diffeomorphism of leaf spaces.


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