Vol. 74, No. 2, 1978

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

Richard Paul Osborne

Vol. 74 (1978), No. 2, 481–495

Every closed orientable 3-manifold 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.

Mathematical Subject Classification
Primary: 57A10, 57A10
Received: 14 September 1976
Revised: 6 June 1977
Published: 1 February 1978
Richard Paul Osborne