The Number of Minimal Components and Homologically Independent Compact Leaves of a Weakly Generic Morse Form on a Closed Surface

@inproceedings{Gelbukh2011TheNO,
title={The Number of Minimal Components and Homologically Independent Compact Leaves of a Weakly Generic Morse Form on a Closed Surface},
author={Irina Gelbukh},
year={2011}
}

On a closed orientable surface M g of genus g, we consider the foliation of a weakly generic Morse form ω on M g and show that for such forms c(ω) + m(ω) = g − 1 2 k(ω), where c(ω) is the number of homologically independent compact leaves of the foliation, m(ω) is the number of its minimal components, and k(ω) is the total number of singularities of ω that are surrounded by a minimal component. We also give lower bounds on m(ω) in terms of k(ω) and the form rank rk ω or the structure of ker… CONTINUE READING