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Close cohomologous Morse forms with compact leaves

Irina Gelbukh (2013)

Czechoslovak Mathematical Journal

We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave γ , then any close cohomologous form has a compact leave close to γ . Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease...

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