Resumo: Stable maps between surfaces can only have fold curves with isolated cusp points on them (H. Whitney [1]). The global description of a stable map between closed surfaces requires the determination of both, the topological type of its regular set in the domain and the isotopy type of the image of its singular set (branch set or apparent contour) in the range surface. In [3] we considered stable maps between non orientable surfaces and attached them conveniently defined graphs that extend the idea of graph between surfaces in the oriented case [2, 4]. We proved that any weighted graph with non-negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane. More recent work on this subject, we focalize our attention in the particular case of planar fold maps including the non orientable case. We shall thus consider stable maps from closed (non necessarily oriented) surfaces to the projective plane and will extend the class of graphs previously defined in a way that enables us to distinguish among orientable and non-orientable regions in the complement of the singular set. In this work we will present the necessary and sufficient conditions for such a graph to be attached to a fold map from a closed surface to the projective plane.

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