On the structure of a Morse form foliation

I. Gelbukh

Displaying similar documents to “On the structure of a Morse form foliation”

Close cohomologous Morse forms with compact leaves

Irina Gelbukh (2013)

Czechoslovak Mathematical Journal

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We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave $γ$ , then any close cohomologous form has a compact leave close to $γ$ . Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves...

Maximal ideals in Loc (M,F).

Robert Wolak (1987)

Collectanea Mathematica

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Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, $C^{2}$ -foliated manifolds of codimension one, having all leaves proper, are shown to be $C^{\infty}$ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class $C^{\infty}$ . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class $C^{r}$ and of class $C^{r + 1}$ for every nonnegative integer $r$ .

On transverse foliations

Atsushi Sato, Itiro Tamura (1981)

Publications Mathématiques de l'IHÉS

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On the existence of exceptional leaves in foliations of co-dimension one

Richard Sacksteder (1964)

Annales de l'institut Fourier

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Exemples d’une structure feuilletée de co-dimension un, de classe $C^{\infty}$ , dont une feuille est exceptionnelle.

Tischler fibrations of open foliated sets

John Cantwell, Lawrence Conlon (1981)

Annales de l'institut Fourier

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Let $M$ be a closed, foliated manifold, and let $U$ be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which $U$ admits an approximating (Tischler) fibration over $S^{1}$ . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.