Number of Minimal Components and Homologically Independent Compact Leaves for a Morse Form Foliation

Author: Irina Gelbukh

Stud. Sci. Math. Hung., vol. 46, no. 4, pp. 547-557, 2009.

Abstract: 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 $b_1'$. A sharp estimate $0 \le m(\omega) + c(\omega) \le b_1'$ 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.

Keywords: Morse form foliation, minimal components, compact leaves

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