Smooth distributions are finitely generated

Lance Drager, Jeffrey Lee, Efton Park, Ken Richardson

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)13
JournalAnnals of Global Analysis and Geometry
StatePublished - Jul 28 2011

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