Some 3-manifolds with 2-generated fundamental group
type: Item
instance of: scholarly article
title: Some 3-manifolds with 2-generated fundamental group
zbMATH Open document ID: 1041.57008
author: Richard Weidmann
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: For an orientable closed \(3\)-manifold \(M\), the Heegaard genus gives an upper bound for the rank of the fundamental group \(\pi_1(M)\). \textit{M. Boileau} and \textit{H. Zieschang} [Invent. Math. 76, 455--468 (1984; Zbl 0538.57004)] computed the rank of the fundamental groups for some Seifert fibered manifolds and showed that there exists a family of Seifert fibered manifolds with Heegaard genus \(3\) and rank two fundamental group. In this paper, the author constructs a family of graph manifolds consisting of two Seifert fibered manifolds whose orbifolds are the Möbius band with at most one exceptional fiber and the disk with two exceptional fibers. It is shown that these manifolds have Heegaard genus \(3\) and rank two fundamental group. In fact, the examples of Boileau and Zieschang can be considered as a special case of the family here as the union of two Seifert fibered manifolds.
reviewed by: Masakazu Teragaito
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 2051641
zbMATH Keywords: Heegaard genus
zbMATH Keywords: rank
zbMATH Keywords: Seifert fibered manifold
zbMATH Keywords: graph manifold
MaRDI profile type: Publication
full work available at URL: s00013-003-4742-9
OpenAlex ID: W2073932752
DOI: 10.1007/S00013-003-4742-9
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description: scientific article; zbMATH DE number 2051641