The simplest closed 3-manifolds. With an appendix by Osborne and J. Yellen

Abstract

Every closed orientable 3-manifoId has a Heegaard diagram and corresponding group presentations. We shall show here how to give a complete analysis of all closed orientable 3-manifolds that have genus two Heegaard diagrams having a corresponding presentation one of whose relators contains no more than 4 syllables. This is equivalent to saying that one of the determining simple closed curves in the diagram crosses a "waist band" of the diagram no more than 4 times. In the appendix we have given a catalog of manifolds with two generator presentations and not more than 20 syllables.