The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface
Irina Gelbukh · Rocky Mountain Journal of Mathematics · 2013
On a closed orientable surface M 2 of genus g, we consider the foliation of a weakly generic Morse form ! on M 2 and show that for such forms c(!) + m(!) = g 1 k(!), wh ere c(!) is the number of homologically independent compact leaves of the foliation, m(!) is the number of its mini- mal components, and k(!) is the total number of singularities of ! that are surrounded by a minimal component. We also give lower bounds on m(!) in terms of k(!) and the form rank rk! or the structure of ker(!), where (!) is the integration map.