Displaying similar documents to “Orbit projections of proper Lie groupoids as fibrations”

Lie groupoids of mappings taking values in a Lie groupoid

Habib Amiri, Helge Glöckner, Alexander Schmeding (2020)

Archivum Mathematicum

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Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids...

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...

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.