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 -connected leaves and a wide class of -connected leaves by proving a semi-local Levi-Malcev theorem for the semi-simple part of their holonomy Lie algebroid.
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 -connexe et pour une classe importante de feuilles -connexes en démontrant un théorème de Levi-Malcev semi-local pour la partie semi-simple de leur algébroïde de Lie d’holonomie.
Accepted:
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Keywords: Singular foliations, singular leaves, linearizations in control theory, Levi-Malcev theorems, Lie algebroids
Mot clés : Feuilletages singuliers, feuilles singulières, théorie du contrôle et linéarisation, théorèmes de Levi-Malcev, algébroïdes de Lie
@article{JEP_2021__8__1037_0, author = {Laurent-Gengoux, Camille and Ryvkin, Leonid}, title = {The neighborhood of a singular leaf}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique - Math\'ematiques}, pages = {1037--1064}, publisher = {Ecole polytechnique}, volume = {8}, year = {2021}, doi = {10.5802/jep.165}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jep.165/} }
TY - JOUR AU - Laurent-Gengoux, Camille AU - Ryvkin, Leonid TI - The neighborhood of a singular leaf JO - Journal de l’École polytechnique - Mathématiques PY - 2021 SP - 1037 EP - 1064 VL - 8 PB - Ecole polytechnique UR - http://archive.numdam.org/articles/10.5802/jep.165/ DO - 10.5802/jep.165 LA - en ID - JEP_2021__8__1037_0 ER -
%0 Journal Article %A Laurent-Gengoux, Camille %A Ryvkin, Leonid %T The neighborhood of a singular leaf %J Journal de l’École polytechnique - Mathématiques %D 2021 %P 1037-1064 %V 8 %I Ecole polytechnique %U http://archive.numdam.org/articles/10.5802/jep.165/ %R 10.5802/jep.165 %G en %F JEP_2021__8__1037_0
Laurent-Gengoux, Camille; Ryvkin, Leonid. The neighborhood of a singular leaf. Journal de l’École polytechnique - Mathématiques, Volume 8 (2021), pp. 1037-1064. doi : 10.5802/jep.165. http://archive.numdam.org/articles/10.5802/jep.165/
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