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.
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Drager, L.D., Lee, J.M., Park, E. et al. Smooth distributions are finitely generated. Ann Glob Anal Geom 41, 357–369 (2012). https://doi.org/10.1007/s10455-011-9287-8
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DOI: https://doi.org/10.1007/s10455-011-9287-8