On the linearization theorem for proper Lie groupoids
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 46 (2013) no. 5, p. 723-746

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 throughout the existing literature).

Nous revisitons les théorèmes de linéarisation pour les groupoïdes de Lie propres autour des orbites générales. Dans le cas du point fixe (connu sous le nom de théorème de Zung), nous donnons une preuve plus courte et plus géométrique, basée sur l'argument de déformation de Moser. Le passage au cas général est décrit de façon plus conceptuelle, comme manifestation de l'invariance de Morita. Nous clarifions également l'énoncé précis du théorème de linéarisation (la littérature sur ce sujet est assez confuse).

DOI : https://doi.org/10.24033/asens.2200
Classification:  58H05,  57R99,  57S15,  53C12
Keywords: Lie groupoids, proper actions, linearization, foliations, local Reeb stability
@article{ASENS_2013_4_46_5_723_0,
     author = {Crainic, Marius and Struchiner, Ivan},
     title = {On the linearization theorem for proper Lie groupoids},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 46},
     number = {5},
     year = {2013},
     pages = {723-746},
     doi = {10.24033/asens.2200},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2013_4_46_5_723_0}
}
Crainic, Marius; Struchiner, Ivan. On the linearization theorem for proper Lie groupoids. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 46 (2013) no. 5, pp. 723-746. doi : 10.24033/asens.2200. http://www.numdam.org/item/ASENS_2013_4_46_5_723_0/

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