The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface. (English) Zbl 1280.57021

Gelbukh, I.

Rocky Mt. J. Math. 43, No. 5, 1537-1552 (2013).

Let \(M^2_g\) be a closed orientable surface of genus \(g\), and consider the foliation induced on \(M\) by a weakly generic Morse form \(\omega\). The author relates three quantities: the number of homologically independent compact leaves of the foliation, the number of its minimal components, and the total number of singularities of \(\omega\) that are surrounded by a minimal component.

Reviewer: Marta Macho Stadler (Leioa)

MSC:

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

Keywords:

surface; Morse form foliation; minimal component; singularity

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