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...