A geometric description of 'normal' crystallizations
type: Item
instance of: scholarly article
title: A geometric description of 'normal' crystallizations
zbMATH Open document ID: 0559.05027
DOI: 10.1007/BF01223531
author: Luigi Grasselli
published in: Journal of Geometry
publication date: 1985-01-01T00:00:00Z
review text: Suppose G is a graph with edges colored by the elements of C, a set of cardinality n. This coloration induces an n-dimensional pseudocomplex as follows: (1) For each vertex v in G, select an n-simplex \(\sigma\) (v) and label its vertices by C. (2) If vertices v and w are joined by an edge of color c, identify the (n-1) faces of \(\sigma\) (v) and \(\sigma\) (w) opposite to the vertices labeled c. Every closed connected n-manifold can be represented in this way. The paper under review gives a geometric description of a way in which the colored graph generating a manifold can be normalized into a colored graph with certain properties. The results are applied to the study of double-cones and bijoins.
reviewed by: M.Marx
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 3891397
zbMATH Keywords: crystallization
zbMATH Keywords: pseudocomplex
zbMATH Keywords: colored graph
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3891397