Foliations, locally Lie groupoids and holonomy
Ronald Brown, Osman Mucuk (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Displaying similar documents to “Local and nice structures of the groupoid of an equivalence relation”
Foliations, locally Lie groupoids and holonomy
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On the linearization theorem for proper Lie groupoids
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We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated...
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Singular foliations with Ehresmann connections and their holonomy groupoids
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We introduce topological 𝒬-holonomy groupoids for singular foliations (M,ℱ) with an Ehresmann connection 𝒬 using 𝒬-holonomy groups, which have a global character. We show advantage of our groupoids over known ones.