Close cohomologous Morse forms with compact leaves
- 43 Downloads
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 under small perturbation of the form; moreover, for generic forms (Morse forms with each singular leaf containing a unique singularity; the set of generic forms is dense in the space of closed 1-forms) this number is locally constant.
KeywordsMorse form foliation compact leaf cohomology class
MSC 201057R30 58K65
Unable to display preview. Download preview PDF.
- M. Farber: Topology of Closed One-Forms. Mathematical Surveys and Monographs 108. AMS, Providence, RI, 2004.Google Scholar