Presentations of étendues
Anders Kock, Ieke Moerdijk (1991)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Anders Kock, Ieke Moerdijk (1991)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Ieke Moerdijk (1991)
Annales de l'institut Fourier
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For any etale topological groupoid (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space .
Mucuk, Osman, İçen, İlhan (2001)
International Journal of Mathematics and Mathematical Sciences
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Ieke Moerdijk (1990)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Bunge, Marta (2008)
Theory and Applications of Categories [electronic only]
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Jean Pradines (1989)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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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...
Ronald Brown, Osman Mucuk (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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