Lie Groupoids as generalized atlases

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dc.creatorPradines, Jean
dc.date2007-11-13
dc.date.accessioned2026-07-07T08:42:50Z
dc.date.available2026-07-07T08:42:50Z
dc.descriptionStarting 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 and surmersions, yielding a very polymorphous unifying theory. We suggest further developments.
dc.description34 pages, lecture delivered at the 5th Conference on Geometry ans Topology of Manifolds, Krynica (Poland), April 2003
dc.identifierhttps://arxiv.org/abs/0711.2077
dc.identifierhttp://arxiv.org/abs/0711.2077
dc.identifierCEJM 2(5) 2004 624-662
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142105
dc.subjectDifferential Geometry
dc.subjectCategory Theory
dc.subject58H05
dc.titleLie Groupoids as generalized atlases
dc.typetext

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