On the linearization theorem for proper Lie groupoids

Marius Crainic; Ivan Struchiner

Annales scientifiques de l'École Normale Supérieure (2013)

  • Volume: 46, Issue: 5, page 723-746
  • ISSN: 0012-9593

Abstract

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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 throughout the existing literature).

How to cite

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Crainic, Marius, and Struchiner, Ivan. "On the linearization theorem for proper Lie groupoids." Annales scientifiques de l'École Normale Supérieure 46.5 (2013): 723-746. <http://eudml.org/doc/272114>.

@article{Crainic2013,
abstract = {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).},
author = {Crainic, Marius, Struchiner, Ivan},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Lie groupoids; proper actions; linearization; foliations; local Reeb stability},
language = {eng},
number = {5},
pages = {723-746},
publisher = {Société mathématique de France},
title = {On the linearization theorem for proper Lie groupoids},
url = {http://eudml.org/doc/272114},
volume = {46},
year = {2013},
}

TY - JOUR
AU - Crainic, Marius
AU - Struchiner, Ivan
TI - On the linearization theorem for proper Lie groupoids
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2013
PB - Société mathématique de France
VL - 46
IS - 5
SP - 723
EP - 746
AB - 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).
LA - eng
KW - Lie groupoids; proper actions; linearization; foliations; local Reeb stability
UR - http://eudml.org/doc/272114
ER -

References

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