A note on Lie algebroids which arise from groupoid actions
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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Kirill Mackenzie (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Jan Kubarski (1987)
Colloquium Mathematicae
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Ronald Brown, Osman Mucuk (1995)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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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...
Paterson, Alan L.T. (2000)
Homology, Homotopy and Applications
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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...
Tahar Mokri (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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A. Szybiak (1972)
Colloquium Mathematicae
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Jure Kališnik (2011)
Czechoslovak Mathematical Journal
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The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...