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
Link To Document