A graph-theoretical representation of PL-manifolds - A survey on crystallizations

This is a survey of the techniques and results developed by M. Pezzana and his group, which includes, besides the authors, A. Cavicchioli, P. Bandieri and A Donati. The original concept is that of "contracted triangulation", which was introduced with the main goal of finding a "minimal" atlas for topological manifolds ([P1 1968], [P2 1974], [P3 1974], [FG2 1979]). Only later did the possibility of deducing a graph-theoretical tool - the crystallization - for representing P.L. manifolds occur as a major aspect of the theory ([P4 1975], [F1 1976]). This leads to an application of graph theory to P.L. topology, which seems not to have been explored before. Recently, other authors outside Italy have independently become interested in this subject. For the sake of conciseness, definitions and statements often appear in a form other than that of the quoted references. © 1986 Birkhäuser Verlag.