How to define the differentiable graph of a singular foliation

Jean Pradines

Displaying similar documents to “How to define the differentiable graph of a singular foliation”

Local and nice structures of the groupoid of an equivalence relation

Jan Kubarski, Tomasz Rybicki (2004)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Morphisms between spaces of leaves viewed as fractions

Jean Pradines (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Lie groupoids as generalized atlases

Jean Pradines (2004)

Open Mathematics

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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...