## Institute for Mathematical Sciences

## Preprint ims95-4

** Y. Moriah & J. Schultens **
* Irreducible Heegaard Splittings of Seifert Fibered Spaces are Either Vertical or Horizontal *

Abstract: Irreducible 3-manifolds are divided into Haken manifolds and non-Haken manifolds. Much is known about the Haken manifolds and this knowledge has been obtained by using the fact that they contain incompressible surfaces. On the other hand, little is known about non-Haken manifolds. As we cannot make use of incompressible surfaces we are forced to consider other methods for studying these manifolds. For example, exploiting the structure of their Heegaard splittings. This approach is enhanced by the result of Casson and Gordon [CG1] that irreducible Heegaard splittings are either strongly irreducible (see Definition 1.2) or the manifold is Haken. Hence, the study of Heegaard splittings as a mean of understanding 3-manifolds, whether they are Haken or not, takes on a new significance.

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