Journal of Differential Geometry

Holonomy Groupoids of Singular Foliations

Claire Debord

Abstract

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.

Article information

Source
J. Differential Geom. Volume 58, Number 3 (2001), 467-500.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090348356

Digital Object Identifier
doi:10.4310/jdg/1090348356

Mathematical Reviews number (MathSciNet)
MR1906783

Zentralblatt MATH identifier
1034.58017

Citation

Debord, Claire. Holonomy Groupoids of Singular Foliations. J. Differential Geom. 58 (2001), no. 3, 467--500. doi:10.4310/jdg/1090348356. https://projecteuclid.org/euclid.jdg/1090348356.


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