Smooth distributions are finitely generated

Lance D. Drager, Jeffrey M. Lee, Efton Park, Ken Richardson

Research output: Contribution to journalArticle

13 Scopus citations

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)357-369
Number of pages13
JournalAnnals of Global Analysis and Geometry
Volume41
Issue number3
DOIs
StatePublished - Mar 2012

Keywords

  • Distributions
  • Foliations

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