• Title of article

    Codimension one foliations without unstable compact leaves

  • Author/Authors

    Firmo، نويسنده , , S. and Sarmiento، نويسنده , , A.، نويسنده ,

  • Issue Information
    دوماهنامه با شماره پیاپی سال 1997
  • Pages
    21
  • From page
    247
  • To page
    267
  • Abstract
    On a smooth (C∞) closed manifold M every smooth codimension one foliation which is a limit in the C0-topology of foliations defined by fibrations F ↬ M → S1 with H1(F; R) = {0} has a compact leaf. From this result some others are obtained about genericity in the Cr-topology(r = 0, 1) with respect to the foliations with finitely many compact leaves which are all Cr-stable. The main result is a type of Kupka-Smale theorem for codimension one foliations: the set of all codimension one foliations whose compact leaves are C∞-stable is a Gδ-dense set in the space of all transversely orientable codimension one foliations on M endowed with the C∞-topology.
  • Keywords
    Stable leaf , Genericity , Codimension one foliation
  • Journal title
    Topology and its Applications
  • Serial Year
    1997
  • Journal title
    Topology and its Applications
  • Record number

    1579175