Holonomy groupoids of singular foliations.
type: Item
instance of: scholarly article
title: Holonomy groupoids of singular foliations.
zbMATH Open document ID: 1034.58017
author: Claire Debord
published in: Journal of Differential Geometry
publication date: 2002-08-15T00:00:00Z
review text: The author presents a new construction of Lie groupoids which is particularly well adapted to the generalization of holonomy groupoids of singular foliations. Given a family of local Lie groupoids on open subsets of a manifold satisfying certain conditions, she constructs a Lie groupoid that contains the whole family. This construction involves a new way of considering local Morita equivalences, not only as equivalence relations but also as generalized isomorphisms. This enables the author to prove, among others, that almost injective Lie algebroids are integrable. In conclusion, several interesting concrete examples are discussed.
Mathematics Subject Classification ID: 58H05
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 1782696
zbMATH Keywords: Lie groupoid
zbMATH Keywords: singular foliation
zbMATH Keywords: Morita equivalence
zbMATH Keywords: Lie algebroid
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1090348356
OpenAlex ID: W2170256719
Wikidata QID: Q115202256
DOI: 10.4310/JDG/1090348356
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description: scientific article; zbMATH DE number 1782696