Heegaard splittings of Seifert fibered spaces (Q1106512)

This paper gives a classification theorem of genus two Heegaard splittings of Seifert fibered spaces over \(S^ 2\) with three exceptional fibers, except for when two of the exceptional fibers have the same invariants with opposite orientation. The main idea was to distinguish between the Heegaard splittings by distinguishing between the Nielsen equivalence classes of pairs of generators for the fundamental group of the manifold determined by them. Distinguishing Nielsen equivalence classes in groups which are not one relator groups is an algebraic result in its own right.