Pré-Publication, Document De Travail Année : 2021

AN INTEGRABILITY CRITERION FOR A PROJECTIVE LIMIT OF BANACH DISTRIBUTIONS

Résumé

We give an integrability criterion for a projective limit of Banach distributions on a Fréchet manifold which is a projective limit of Banach manifolds. This leads to a result of integrability of projective limit of involutive bundles on a projective sequence of Banach manifolds. This can be seen as a version of Frobenius Theorem in Fréchet setting. As consequence, we obtain a version of the third Lie theorem for a Fréchet-Lie group which is a submersive projective limit of Banach Lie groups. We also give an application to a sequence of prolongations of a Banach Lie algebroid.

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Dates et versions

hal-03207038 , version 1 (23-04-2021)

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  • HAL Id : hal-03207038 , version 1

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Fernand Pelletier. AN INTEGRABILITY CRITERION FOR A PROJECTIVE LIMIT OF BANACH DISTRIBUTIONS. 2021. ⟨hal-03207038⟩
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