Paintings: A planar approach to higher dimensions

A painting in dimension n is an object induced by certain regular (n+1)-colored finite graphs. Some classes of paintings are shown to be plane universal models for closed n-manifolds. Ferri and Gagliardi's equivalence theorem (graph-theoretical counterpart for homeomorphisms) [5], and Ferri's strengthening of their result [3] are used to provide a surprisingly simple way to state the equivalence theorem: the restricted crystallization moves [3] become deletion and insertion of one edge in certain plane graphs. Various new properties of minimum 3-crystallizations are obtained in the framework of paintings. Two conjectures related to the recognition of the 3-sphere are included.This work was performed under the support of UFPE, FINEP and CNPq (contract no. 30.1103/80).