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arXiv · 1311.1414

A continuous deRham antidifferential

Manuel Araujo·Gustavo Granja
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Abstract

Let M be a manifold, possibly with boundary. We show that the deRham differential from k-forms to exact (k+1)-forms has a continuous right inverse when both spaces are given the weak Whitney topology. This antidifferential operator is given a fairly explicit formula depending on the choice of a suitable good cover of M and local coordinates on the elements of the cover. If the antidifferential operator is applied to a smooth family of exact forms, it produces a smooth family of forms.

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Manuel Araujo, Gustavo Granja. 2014-04-10. A continuous deRham antidifferential. https://arxiv.org/abs/1311.1414

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