Topological Invariants of Stable Maps from a Surface to the Plane from a Global Viewpoint

We associate to any stable map of a surface M to the plane certain global invariants: the first is a weighted graph which describes the pair M, Σf (where Σf is the singular set of f). The other is a Vassiliev type invariant related to the number of connected components of Σf. We describe this invariant in terms of Chíncaro’s classification singularities of codimension one of maps between surfaces.