Conditions and a criterion for the presence of minimal components in the foliation of a Morse form Ï‰ n a smooth closed oriented manifold M are given in terms of (1) the maximum rank of a subgroup inâ€¦ (More)

The foliation of a Morse form Ï‰ on a closed manifold M is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated.â€¦ (More)

On a closed orientable surface M g of genus g, we consider the foliation of a weakly generic Morse form Ï‰ on M g and show that for such forms c(Ï‰) + m(Ï‰) = g âˆ’ 1 2 k(Ï‰), where c(Ï‰) is the number ofâ€¦ (More)

On a smooth closed n-manifold, we consider Morse forms with wedge-product zero; we call such forms collinear. This is an equivalence relation. Collinearity classes are classified by the underlyingâ€¦ (More)

The numbers m(Ï‰) of minimal components and c(Ï‰) of homologically independent compact leaves of the foliation of a Morse form Ï‰ on a connected smooth closed oriented manifold M are studied in terms ofâ€¦ (More)

We study the topology of foliations of close cohomologous Morse forms on a smooth closed oriented manifold. We show that if a closed form has a compact leave Î³, then any close cohomologous form has aâ€¦ (More)

We study the maximal ranks of a free and a free abelian quotients of a finitely generated group, called co-rank (inner rank, cut number) and the Betti number, respectively. We show that anyâ€¦ (More)

Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lowerâ€¦ (More)

We study one-forms with zero wedge-product, which we call ollinear, and their foliations. We characterise the set of forms that define a given foliation, w ith special attention to closed forms andâ€¦ (More)