Open Access
July, 2001 Holonomy Groupoids of Singular Foliations
Claire Debord
J. Differential Geom. 58(3): 467-500 (July, 2001). DOI: 10.4310/jdg/1090348356


We give a new construction of Lie groupoids which is particularly well adapted to the generalization of holonomy groupoids to singular foliations. Given a family of local Lie groupoids on open sets of a smooth manifold M, satisfying some hypothesis, we construct a Lie groupoid which 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. In particular we prove that almost injective Lie algebroids are integrable.


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Claire Debord. "Holonomy Groupoids of Singular Foliations." J. Differential Geom. 58 (3) 467 - 500, July, 2001.


Published: July, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1034.58017
MathSciNet: MR1906783
Digital Object Identifier: 10.4310/jdg/1090348356

Rights: Copyright © 2001 Lehigh University

Vol.58 • No. 3 • July, 2001
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