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Keywords:
number of minimal components; number of maximal components; compact leaves; foliation graph; rank of a form
number of minimal components; number of maximal components; compact leaves; foliation graph; rank of a form
Summary:
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.
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