Number of minimal components and homologically independent compact leaves for a Morse form foliation. (English) Zbl 1274.57005

Gelbukh, Irina

Stud. Sci. Math. Hung. 46, No. 4, 547-557 (2009).

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.

MSC:

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

Keywords:

Morse form foliation; minimal components; compact leaves