Smooth distributions are finitely generated

Details Smooth distributions are finitely generated Smooth distributions are finitely generated

2010-12-27

arxiv.org/abs/1012.5641v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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