On minimum genus Heegaard splittings of some orientable closed 3-manifolds
This paper is concerned with the genus and the total number of minimal Heegaard surfaces in those closed 3-manifolds M obtained by glueing together two Seifert fibre spaces over the disc with two exceptional fibres. A unified proof is presented for the known characterization of those glueing homeomorphisms yielding Heegaard genus two 3-manifolds [see also \textit{T. Kobayashi}, Osaka J. Math. 21, 437-455 (1984; Zbl 0568.57007); and \textit{M. Boileau} and \textit{H. Zieschang}, Invent. Math. 76, 455-468 (1984; Zbl 0538.57004)]. Moreover, it is shown that any 3- manifold M, as above, contains at most four non-isotopic minimal Heegaard surfaces. A construction for all possible candidates is given. It is further discussed for which glueing homeomorphism these candidates actually occur.
glueing together two Seifert fibre spaces
scientific article; zbMATH DE number 4176011