Universal coverings of PL-manifolds via coloured graphs
type: Item
instance of: scholarly article
title: Universal coverings of PL-manifolds via coloured graphs
zbMATH Open document ID: 0764.57004
DOI: 10.1007/BF01834205
author: Antonio F. Costas
author: Luigi Grasselli
published in: Aequationes Mathematicae
publication date: 1993-01-06T00:00:00Z
full work available at URL: https://eudml.org/doc/137480
review text: The authors use the representation of piecewise linear manifolds by means of edge-coloured graphs [see, e.g., \textit{M. Ferri, C. Gagliardi} and \textit{L. Grasselli}, Aequationes Math. 31, 121-141 (1986; Zbl 0623.57012)]. This approach together with some results concerning universal covering maps allow one to construct an infinite ball complex \(P(n)\), \(n>1\), such that every orientable PL \(n\)-manifold is a quotient of the polyhedron underlying \(P(n)\) under the action of a finite index subgroup of a certain Fuchsian group. Then the authors introduce a combinatorial invariant of a closed connected PL manifold \(M\), called the type of \(M\), and prove some results about the calculation of this invariant for surfaces and manifolds of dimension 3.
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 85812
zbMATH Keywords: coloured map
zbMATH Keywords: type of a manifold
zbMATH Keywords: representation of piecewise linear manifolds by edge-coloured graphs
zbMATH Keywords: three-manifold
zbMATH Keywords: universal covering maps
zbMATH Keywords: type
zbMATH Keywords: surfaces
reviewed by: Alberto Cavicchioli
MaRDI profile type: Publication
cites work: The combinatorics of colored triangulations of manifolds
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cites work: Q3266916
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cites work: The embeddings of a graph—A survey
OpenAlex ID: W2005797899
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description: scientific article; zbMATH DE number 85812