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research group in Geometric Topology via Graphs Encoding ManifoldS


Since the 1970s, at the University of Modena, Mario Pezzana and his research group have created a novel representation theory of PL manifolds, which makes use of edge-colored graphs, dual to colored triangulations. Later, the theory was developed by various researchers around the world, but the Modenese group maintained a central role, both for the discovery of new results, and for the study of the interconnections with other disciplines.

The representing objects are usually called GEMS , i.e. Graphs Encoding ManifoldS. For this reason, GEMS also identifies the research group itself.    

Moreover, GEM theory is often known as CRYSTALLIZATION theory,  from the name of a special kind of representing objects (crystallizations), which are proved to exist for each compact PL-manifold, in arbitrary dimension. 



Examples of colored triangulations and edge-colored graphs representing manifolds, in dimension 2: