A geometric description of 'normal' crystallizations
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.
scientific article; zbMATH DE number 3891397
scientific article