On compact leaves of a Morse form foliation. (English) Zbl 1240.57011

Gelbukh, Irina

Publ. Math. Debr. 78, No. 1, 37-48 (2011).

The author presents a short and nice study of co-dimension 1 foliations defined by closed 1-forms \(\omega\) arising as differentials of Morse functions (non-degenerate singularities) on a compact, oriented, connected smooth \(n\)-dimensional manifold \(M\). She gives criteria for such foliations to have a compact leaf, to have \(k\) homologically independent compact leaves, and to have no minimal components.

Reviewer: Vagn Lundsgaard Hansen (Lyngby)

MSC:

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

Keywords:

Morse form foliation; compact leaves; collinear 1-forms; form rank