Smooth distributions are finitely generated
Differential Geometry
2021-01-28 v1
Abstract
A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely generated as a module over the smooth functions. Our results are valid in greater generality, where the tangent bundle may be replaced by an arbitrary vector bundle.
Keywords
Cite
@article{arxiv.1012.5641,
title = {Smooth distributions are finitely generated},
author = {Lance D. Drager and Jeffrey M. Lee and Efton Park and Ken Richardson},
journal= {arXiv preprint arXiv:1012.5641},
year = {2021}
}
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13 pages