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Number of minimal components and homologically independent compact leaves for a Morse form foliation. (English) Zbl 1274.57005
Summary: The numbers $$m(\omega)$$ of minimal components and $$c(\omega)$$ of homologically independent compact leaves of the foliation of a Morse form $$\omega$$ on a connected smooth closed oriented manifold $$M$$ are studied in terms of the first non-commutative Betti number $$b'_1(M)$$. A sharp estimate $$0 \leqq m(\omega) + c(\omega) \leqq b'_1(M)$$ is given. It is shown that all values of $$m(\omega)+c(\omega)$$, and in some cases all combinations of $$m(\omega)$$ and $$c(\omega)$$ with this condition, are reached on a given $$M$$. The corresponding issues are also studied in the classes of generic forms and compactifiable foliations.

##### MSC:
 57R30 Foliations in differential topology; geometric theory 58K65 Topological invariants on manifolds
##### Keywords:
Morse form foliation; minimal components; compact leaves
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