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:
Published online:
Keywords: Singular foliations, singular leaves, linearizations in control theory, Levi-Malcev theorems, Lie algebroids
Mots-clés : Feuilletages singuliers, feuilles singulières, théorie du contrôle et linéarisation, théorèmes de Levi-Malcev, algébroïdes de Lie
Camille Laurent-Gengoux 1; Leonid Ryvkin 2, 3, 4
CC-BY 4.0
@article{JEP_2021__8__1037_0,
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/}
}
TY - JOUR AU - Camille Laurent-Gengoux AU - Leonid Ryvkin TI - The neighborhood of a singular leaf JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1037 EP - 1064 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.165/ DO - 10.5802/jep.165 LA - en ID - JEP_2021__8__1037_0 ER -
%0 Journal Article %A Camille Laurent-Gengoux %A Leonid Ryvkin %T The neighborhood of a singular leaf %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 1037-1064 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.165/ %R 10.5802/jep.165 %G en %F JEP_2021__8__1037_0
Camille Laurent-Gengoux; Leonid Ryvkin. The neighborhood of a singular leaf. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 1037-1064. doi : 10.5802/jep.165. https://jep.centre-mersenne.org/articles/10.5802/jep.165/
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