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arXiv · 2105.00245

An integrability criterion for a projective limit of Banach distributions

Fernand Pelletier
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Abstract

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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Fernand Pelletier. 2021-05-01. An integrability criterion for a projective limit of Banach distributions. https://doi.org/10.1016/j.geomphys.2022.104453

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