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On the structure of a Morse form foliation. (English) Zbl 1224.57010
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 $$\operatorname {rk} \omega$$ and $$\operatorname {Sing} \omega$$. 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 foliation graph being a tree.

##### MSC:
 57R30 Foliations in differential topology; geometric theory 58K65 Topological invariants on manifolds
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