Structure of a Morse Form Foliation on a Closed Surface in Terms of Genus

Author: Irina Gelbukh

Differ. Geom. Appl., vol. 29, no. 4, 2011, pp. 473--492.

Abstract: We study the geometry of compact singular leaves $\gamma$ and minimal components $C^{min}$ of the foliation $F$ of a Morse form $\omega$ on $M^2_g$ in terms of genus $g(\cdot)$. We show that $c(\omega) + \sum_\gamma g(V(\gamma)) + g(\bigcup \overline {C^{min}})=g$, where $c(\omega)$ is the number of homologically independent compact leaves and $V(\cdot)$ is a small closed tubular neighborhood. This allows us to prove a criterion for compactness of the singular foliation $\overline F$, to estimate the number of its minimal components, and to give an upper bound on the rank $rk \omega$, in terms of genus.

Keywords: Morse form foliation; minimal component; compact singular leave; genus; isotropic subgroup

PDF: Structure of a Morse Form Foliation on a Closed Surface in Terms of Genus (preprint version)

Final text on the journal's site: DOI 10.1016/j.difgeo.2011.04.029.