On minimum genus Heegaard splittings of some orientable closed 3-manifolds
type: Item
instance of: scholarly article
title: On minimum genus Heegaard splittings of some orientable closed 3-manifolds
zbMATH Open document ID: 0714.57007
author: Kanji Morimoto
published in: Tokyo Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 4176011
zbMATH Keywords: minimal Heegaard surfaces
zbMATH Keywords: closed 3-manifolds
zbMATH Keywords: glueing together two Seifert fibre spaces
zbMATH Keywords: Heegaard genus two 3-manifolds
zbMATH Keywords: non-isotopic minimal Heegaard surfaces
reviewed by: Klaus Johannson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133184
OpenAlex ID: W2002710166
DOI: 10.3836/TJM/1270133184
description: scientific article; zbMATH DE number 4176011