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Holonomy groupoids of singular foliations. (English) Zbl 1034.58017
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.
Reviewer: I. Kolář (Brno)

MSC:
58H05 Pseudogroups and differentiable groupoids
57R30 Foliations in differential topology; geometric theory
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