Czech Math J., 63(2):515-528, 2013.
Abstract: We study the topology of foliations of close cohomologous Morse forms on a smooth closed oriented manifold. We show that if a closed form has a compact leave $\g$, then any close cohomologous form has a compact leave close to g. Then we prove that the set of Morse forms with compactifiable foliations is open in a cohomology class, and the number of homologically independent compact leaves does not decrease under small perturbation of the form; moreover, for generic forms this number is locally constant.
Keywords: Morse form foliation, compact leaves, cohomology class
PDF: Close cohomologous Morse forms with compact leaves
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