Universal connections on Lie groupoids.
Vassiliou, Efstathios, Nikolopoulos, Apostolos (2003)
International Journal of Mathematics and Mathematical Sciences
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Vassiliou, Efstathios, Nikolopoulos, Apostolos (2003)
International Journal of Mathematics and Mathematical Sciences
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Kirill Mackenzie (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Kirill Mackenzie (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Ivan Kolář (2007)
Banach Center Publications
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For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.
Ronald Brown, Osman Mucuk (1995)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Anders Kock (2007)
Banach Center Publications
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We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.
Jean Pradines (2007)
Banach Center Publications
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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...
Jean-Louis Tu, Ping Xu, Camille Laurent-Gengoux (2004)
Annales scientifiques de l'École Normale Supérieure
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R. A. Bowshell (1971)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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