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The classification of Heegaard splittings for (compact orientable surface)$$\times S^ 1$$. (English) Zbl 0789.57012
The Heegaard splittings of (compact orientable surface)$$\times S^ 1$$ are shown to be stabilizations of Heegaard splittings obtained by an explicit construction. The proof of the classification theorem proceeds by induction. It uses thin presentation techniques for an analysis of the foliations, with respect to a Morse function induced by a Heegaard splitting, of “vertical” annuli and tori.

##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M99 General low-dimensional topology 57R30 Foliations in differential topology; geometric theory
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