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The Reeb graph of a smooth function on a connected smooth closed orientable n-manifold is obtained by contracting the connected components of the level sets to points. The number of loops in the Reeb… Continue Reading
Conditions and a criterion for the presence of minimal components in the foliation of a Morse form ω on a smooth closed oriented manifold M are given in terms of (1) the maximum rank of a subgroup in… Continue Reading
The foliation of a Morse form ω 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.… Continue Reading
We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has… Continue Reading
Sharp bounds are given that connect split points — conic singularities of a special type — of a Morse form with the global structure of its foliation.
A subspace or subgroup is isotropic under a bilinear map if the restriction of the map on it is trivial. We study maximal isotropic subspaces or subgroups under skew-symmetric maps, and in particular… Continue Reading
Abstract We study the geometry of compact singular leaves γ and minimal components C min of the foliation F ω of a Morse form ω on a genus g closed surface M g 2 in terms of genus g ( ⁎ ) . We show… Continue Reading
Abstract 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… Continue Reading
For a connected locally path-connected topological space $X$ and a continuous function $f$ on it such that its Reeb graph $R_f$ is a finite topological graph, we show that the cycle rank of $R_f$,… Continue Reading
The numbers m ( ω ) of minimal components and c ( ω ) of homologically independent compact leaves of the foliation of a Morse form ω on a connected smooth closed oriented manifold M are studied in… Continue Reading