Neuwirth manifolds and colourings of graphs
type: Item
instance of: scholarly article
title: Neuwirth manifolds and colourings of graphs
zbMATH Open document ID: 0772.57021
DOI: 10.1007/BF01830977
published in: Aequationes Mathematicae
publication date: 1993-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137490
review text: Let \(M\) be a prime, orientable, connected, closed 3-manifold. A construction is described associating to certain Heegaard diagrams of \(M\) coloured graphs one of which represents \(M\) in the sense that the realisation of a simplicial complex obtained from the graph is homeomorphic to \(M\). These graphs are then used to classify a family of manifolds introduced by \textit{L. Neuwirth} [``An algorithm for the construction 3-manifolds from 2-complexes'', Proc. Camb. Philos. Soc. 64, 603-613 (1968; Zbl 0162.276)] as Seifert fibred spaces.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 149469
zbMATH Keywords: 3-manifold
zbMATH Keywords: Heegaard diagrams
zbMATH Keywords: simplicial complex
zbMATH Keywords: Seifert fibred spaces
author: Alberto Cavicchioli
reviewed by: David B. Gauld
MaRDI profile type: Publication
cites work: Q3492411
cites work: Generating all orientable n-manifolds from (n-1)-complexes
cites work: Heegaard genus of closed orientable Seifert 3-manifolds
cites work: Q3900685
cites work: Crystallisations of 2-Fold Branched Coverings of S 3
cites work: Crystallisation moves
cites work: A graph-theoretical representation of PL-manifolds -- a survey on crystallizations
cites work: Extending the Concept of Genus to Dimension N
cites work: Q3971219
cites work: Some Historical and Intuitive Aspects of Graph Theory
cites work: Q4114528
cites work: Q3877854
cites work: Q5545839
cites work: Q3888191
cites work: Seifert manifolds
cites work: Q4074117
cites work: Three-Dimensional Manifolds and Their Heegaard Diagrams
cites work: Q3900682
cites work: On irreducible 3-manifolds which are sufficiently large
description: scientific article; zbMATH DE number 149469