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

This is a survey of the techniques and results developped by Mario Pezzana and his group. The original concept is that of "contracted triangualtion", which was introduced with the main goal of finding a "minimal atlas" for compact manifolds. Only later did the possibility of deducing a graph theoretical tool - the crystallization - for representig PL manifolds occur as a mayor aspect of the theory. This leads to an application of graph theory to PL topology, which seems not to have been explored before. Note that many other authors outside Italy have independently become interested in this subject.