# Properties of Morse forms that determine compact foliations on $M_g^2$

**Author:** Irina Mel'nikova

Math. Notes, vol. 60, no. 6, pp. 714-716, 1996.

**Abstract:** In [1, 2] P. Arnoux
and G. Levitt showed that the topology of the foliation of a Morse form
$\omega$ on a compact manifold is closely related to the structure of the
integration mapping $[\omega]:
H_1(M) \to R$.* *
In this paper we consider the
foliation of a Morse form on a two-dimensional manifold $M_g^2$. We study
the relationship of the subgroup $Ker [\omega]
\subset H_1(M_g^2)$* *
with the topology of the foliation.
We consider the structure of the subgroup
$Ker [\omega]$ for a compact foliation and prove a
criterion for the compactness of a foliation.

**Keywords:** Two-dimensional manifold, foliation, Morse form,
integration over cycles

**PDF:** Properties of Morse forms that determine compact foliations on $M_g^2$

**This stub file is intended only for indexing. Please see more details and errata on the author's home page.**