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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.

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.

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Accepted:
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DOI: 10.5802/afst.1617
Classification: 58A30,  18A30,  46T05,  17B66,  37K30,  22E65
Keywords: Integrable distribution, direct limit, convenient structures, almost Lie Banach algebroid, almost Lie bracket, Koszul connection, anchor range
Patrick Cabau 1; Fernand Pelletier 2

1 Lycée Pierre de Fermat, Parvis des Jacobins, 31000 Toulouse, France
2 Lama, Université de Savoie Mont Blanc, 73376 Le Bourget du Lac Cedex, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     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},
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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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