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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.

The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface