GENUS TWO HEEGAARD SPLITTINGS OF ORIENTABLE THREE-MANIFOLDS

HYAM RUBINSTEIN MARTIN SCHARLEMANN

Abstract. It is known that any two genus one Heegaard splittings of the same manifold (typically a lens space) are isotopic. On the other hand, it is known that certain Seifert manifolds have distinct genus two Heegaard splittings. In a previous paper we presented a technique for comparing Heegaard splittings of the same manifold and, using this technique, derived the Bonahon-Otal uniqueness theorem for lens space splittings as a simple corollary. The intent of this paper is to use a similar technique to examine, in general, ways in which two non-isotopic genus two Heegaard splittings of the same 3-manifold are related.