The neighborhood of a singular leaf
[Le voisinage d’une feuille singulière]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1037-1064.

Un résultat important concernant les feuilletages réguliers est leur trivialité semi-locale formelle au voisinage des feuilles simplement connexes. Nous étendons ce résultat aux feuilletages singuliers pour toute feuille 2-connexe et pour une classe importante de feuilles 1-connexes en démontrant un théorème de Levi-Malcev semi-local pour la partie semi-simple de leur algébroïde de Lie d’holonomie.

An important result for regular foliations is their formal semi-local triviality near simply connected leaves. We extend this result to singular foliations for all 2-connected leaves and a wide class of 1-connected leaves by proving a semi-local Levi-Malcev theorem for the semi-simple part of their holonomy Lie algebroid.

Reçu le :
Accepté le :
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DOI : https://doi.org/10.5802/jep.165
Classification : 53C12,  57R30,  93B18
Mots clés : Feuilletages singuliers, feuilles singulières, théorie du contrôle et linéarisation, théorèmes de Levi-Malcev, algébroïdes de Lie
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     author = {Camille Laurent-Gengoux and Leonid Ryvkin},
     title = {The neighborhood of a singular leaf},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {1037--1064},
     publisher = {\'Ecole polytechnique},
     volume = {8},
     year = {2021},
     doi = {10.5802/jep.165},
     language = {en},
     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.165/}
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Camille Laurent-Gengoux; Leonid Ryvkin. The neighborhood of a singular leaf. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1037-1064. doi : 10.5802/jep.165. https://jep.centre-mersenne.org/articles/10.5802/jep.165/

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