Integrability on Direct Limits of Banach Manifolds

Cabau, Patrick; Pelletier, Fernand

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 5, pp. 909-956.

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.

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.

Classification : 58A30, 18A30, 46T05, 17B66, 37K30, 22E65
Mots clés : Integrable distribution, direct limit, convenient structures, almost Lie Banach algebroid, almost Lie bracket, Koszul connection, anchor range

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