A Heegaard splitting of an orientable closed connected 3-manifold M is a closed connected orientable surface F imbedded in M and dividing M into two handlebodies. The genus of the Heegaard splitting is the genus of F and the The aim of this paper is to calculate the Heegaard genus of almost all closed orientable Seifert-manifolds and the rank of their fundamental group. In most of the cases these numbers coincide; however there are counterexamples, as mentioned above, and some cases still remain undecided.
Heegaard genus of M, h(M),
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