Surface maps and n-dimensional manifolds

The main purpose of the paper is to present a standar method for associating a class of "surface maps" to each closed piecewise- linear manifold M^n. Since this class (in fact each map belonging to it) completely represents M^n, then it is possible to produce invariants, through the peculiar properties of the above maps. In particular, two such invariants are presented, together with a brief survey on the main results and problems about them.