In this paper, we study several objects in the framework of direct limits of anchored Banach bundles over particular convenient manifolds (direct limits of Banach manifolds). In particular, we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anchor ranges.
Dans cet article, on s’intéresse à l’étude de divers objets rencontrés dans le cadre de limites directes de fibrés de Banach, munis d’une ancre, au dessus de certaines variétés apparaissant comme limites directes de variétés de Banach. En particulier, on donne un critère d’intégrabilité pour des distributions sur de telles variétés qui sont localement des limites directes de suites particulières d’images d’ancres banachiques.
Accepted:
Published online:
DOI: 10.5802/afst.1617
Keywords: Integrable distribution, direct limit, convenient structures, almost Lie Banach algebroid, almost Lie bracket, Koszul connection, anchor range
Patrick Cabau 1; Fernand Pelletier 2
CC-BY 4.0
@article{AFST_2019_6_28_5_909_0,
author = {Patrick Cabau and Fernand Pelletier},
title = {Integrability on {Direct} {Limits} of {Banach} {Manifolds}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {909--956},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 28},
number = {5},
year = {2019},
doi = {10.5802/afst.1617},
zbl = {1414.53074},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1617/}
}
TY - JOUR AU - Patrick Cabau AU - Fernand Pelletier TI - Integrability on Direct Limits of Banach Manifolds JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 909 EP - 956 VL - 28 IS - 5 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1617/ DO - 10.5802/afst.1617 LA - en ID - AFST_2019_6_28_5_909_0 ER -
%0 Journal Article %A Patrick Cabau %A Fernand Pelletier %T Integrability on Direct Limits of Banach Manifolds %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 909-956 %V 28 %N 5 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1617/ %R 10.5802/afst.1617 %G en %F AFST_2019_6_28_5_909_0
Patrick Cabau; Fernand Pelletier. Integrability on Direct Limits of Banach Manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 5, pp. 909-956. doi : 10.5802/afst.1617. https://afst.centre-mersenne.org/articles/10.5802/afst.1617/
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