Displaying similar documents to “In Ehresmann's footsteps: from group geometries to groupoid geometries”

Functorial prolongations of Lie groupoids

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.

On the linearization theorem for proper Lie groupoids

Marius Crainic, Ivan Struchiner (2013)

Annales scientifiques de l'École Normale Supérieure

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We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated...

Principal bundles, groupoids, and connections

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.