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On Heegaard diagrams of 3-manifolds. (English) Zbl 0674.57010
On the geometry of differentiable manifolds, Workshop, Rome/Italy 1986, Astérisque 163-164, 247-280 (1988).
[For the entire collection see Zbl 0666.00013.]
The text is a survey of some parts of the theory of Heegaard decompositions of three dimensional manifolds. Particular emphasis is on Heegaard decompositions of Seifert fibre spaces. These are sufficiently tractable to provide explicit examples for the following phenomena: (1) Heegaard decompositions are not unique in general (Boileau, Collins, Zieschang, extending earlier examples of Birman, Gonzales-Acuna, Montesinos). (2) The minimal genus of Heegaard decompositions may be strictly bigger than the minimal number of generators for the fundamental group (Boileau, Zieschang).
Reviewer: F.Waldhausen

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