A continuous deRham antidifferential
Differential Geometry
2014-04-11 v2
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.
Keywords
Cite
@article{arxiv.1311.1414,
title = {A continuous deRham antidifferential},
author = {Manuel Araujo and Gustavo Granja},
journal= {arXiv preprint arXiv:1311.1414},
year = {2014}
}
Comments
This paper has been withdrawn because it has become an appendix in arxiv:1404.2433