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.


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