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 :
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