Riemannian foliations and quasifolds

Lin, Yi; Miyamoto, David

doi:10.1007/s00209-024-03595-5

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Riemannian foliations and quasifolds

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Miyamoto, David
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2309.15166
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https://doi.org/10.1007/s00209-024-03595-5
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Lin, Y., & Miyamoto, D. (2024). Riemannian foliations and quasifolds. Mathematische Zeitschrift, 308(3): 49. doi:10.1007/s00209-024-03595-5.

Cite as: https://hdl.handle.net/21.11116/0000-000F-BC70-F

Abstract

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, the leaf space of a Killing Riemannian foliation is a diffeological quasifold: as a diffeological space, it is locally modelled by quotients of Cartesian space by countable groups acting affinely. Furthermore, we prove that the holonomy groupoid of the foliation is, locally, Morita equivalent to the action groupoid of a countable group acting affinely on Cartesian space.