Variétés d'orbites
Lie groupoids as generalized atlases
Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties of embeddings...
Échelles et faisceaux sur les quotients de feuilletages
Morphisms between spaces of leaves viewed as fractions
How to define the differentiable graph of a singular foliation
In Ehresmann's footsteps: from group geometries to groupoid geometries
The geometric understanding of Cartan connections led Charles Ehresmann from the Erlangen program of (abstract) transformation groups to the enlarged program of Lie groupoid actions, via the basic concept of structural groupoid acting through the fibres of a (smooth) principal fibre bundle or of its associated bundles, and the basic examples stemming from the manifold of jets (fibred by its source or target projections). We show that the remarkable relation arising between the actions of the structural...
Pseudo-groupes infinis continus et applications analytiques formelles
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