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Lie groupoids as generalized atlases

  • Review Article
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Central European Journal of Mathematics

Abstract

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 and surmersions, yielding a very polymorphous unifying theory. We suggest further developments.

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Authors and Affiliations

  1. Université Paul Sabatier, 26, rue Alexandre Ducos, F31500, Toulouse, France

    Jean Pradines

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  1. Jean Pradines
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Pradines, J. Lie groupoids as generalized atlases. centr.eur.j.math. 2, 624–662 (2004). https://doi.org/10.2478/BF02475970

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  • DOI: https://doi.org/10.2478/BF02475970

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