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Boileau, M.; Zieschang, Heiner

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

Invent. Math. 76, 455-468 (1984).
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

Cited in 10 Reviews
Cited in 44 Documents

MSC:

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

Keywords:

rank of the fundamental group; Heegaard genus of Seifert 3-manifolds
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\textit{M. Boileau} and \textit{H. Zieschang}, Invent. Math. 76, 455--468 (1984; Zbl 0538.57004)
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References:

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