Journal of Differential Geometry

Holonomy Groupoids of Singular Foliations

Claire Debord


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

First available in Project Euclid: 20 July 2004

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

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