Geodesic
On the structure of a Morse form foliation
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 207-220 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The foliation of a Morse form $\omega$ on a closed manifold $M$ is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of $M$ and $\omega$. Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of $\mathop{\rm rk}\omega $ and ${\rm Sing} \omega $. The set of the ranks of all forms defining a given foliation without minimal components is described. It is shown that if $\omega$ has more centers than conic singularities then $b_1(M)=0$ and thus the foliation has no minimal components and homologically non-trivial compact leaves, its folitation graph being a tree.
The foliation of a Morse form $\omega$ on a closed manifold $M$ is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of $M$ and $\omega$. Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of $\mathop{\rm rk}\omega $ and ${\rm Sing} \omega $. The set of the ranks of all forms defining a given foliation without minimal components is described. It is shown that if $\omega$ has more centers than conic singularities then $b_1(M)=0$ and thus the foliation has no minimal components and homologically non-trivial compact leaves, its folitation graph being a tree.
Classification : 57R30, 58K65
Keywords: number of minimal components; number of maximal components; compact leaves; foliation graph; rank of a form 
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     author = {Gelbukh, I.},
     title = {On the structure of a {Morse} form foliation},
     journal = {Czechoslovak Mathematical Journal},
     pages = {207--220},
     year = {2009},
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     zbl = {1224.57010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a14/}
}
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Gelbukh, I. On the structure of a Morse form foliation. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 207-220. http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a14/