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Heegaard genus of closed orientable Seifert 3-manifolds. (English) Zbl 0538.57004

Für eine geschlossene 3-dimensionale Mannigfaltigkeit M gilt für den Rang r(M) der Fundamentalgruppe und das Heegaard Geschlecht h(M) stets r(M)\(\leq h(M)\). F. Waldhausen stellte 1970 die Frage ob immer \(r(M)=h(M)\) gilt. In der vorliegenden Arbeit wird r(M) und h(M) für fast alle geschlossenen orientierbaren Seifertsche Faserräume M berechnet. In den meisten Fällen ist \(r(M)=h(M)\); es wird aber Waldhausens Frage negativ beantwortet indem gezeigt wird, daß für gewisse Seifertsche Räume M gilt \(2=r(M)<h(M)=3\). Dieses Resultat wurde von den Verff. [C. R. Acad. Sci., Paris, Sér. I 296, 925-928 (1983)] angekündigt.
Reviewer: W.Heil

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M05 Fundamental group, presentations, free differential calculus
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