Tetrahedron manifolds via coloured graphs
type: Item
instance of: scholarly article
title: Tetrahedron manifolds via coloured graphs
zbMATH Open document ID: 0888.57018
DOI: 10.1016/S0012-365X(97)00135-0
author: Luigi Grasselli
author: Salvina Piccarreta
published in: Discrete Mathematics
publication date: 1998-06-07T00:00:00Z
review text: The authors study 3-manifolds of the title previously shown by \textit{E. Molnár} in [Note Mat. 10, No. 2, 335-346 (1990; Zbl 0770.57006)] to be Seifert fiber spaces having fundamental group \(G_{mn}\) with presentation \(P= (x,y\mid x^{m-1} y^{-1} x^{-1} y^{-1}, y^{n-1} x^{-1} y^{-1} x^{-1})\). The paper examines these manifolds from the point-of-view of edge-colored graphs. They show \(P\) is geometric and they reproduce Molnar's result, proving directly that these manifolds are branched 2-sheeted coverings of \(S^3\) with branching set certain links \(L_{mn}\).
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M10
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1121490
zbMATH Keywords: 3-manifold
zbMATH Keywords: geometric presentation
zbMATH Keywords: colored graph
zbMATH Keywords: crystallized structure
reviewed by: Lee P. Neuwirth
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121490