TOPOLOGICAL CLASSIFICATION OF GENERIC REAL MEROMORPHIC FUNCTIONS FROM COMPACT SURFACES
In this article, to each generic real meromorphic function (i.e., having only simple branch points in the appropriate sense) we associate a certain combinatorial gadget which we call the park of a function. We show that the park determines the topological type of the generic real meromorphic function and the set of parks produce an stratification of the space of generic real meromorphic functions. For any of the above topological types, we introduce and calculate the corresponding Hurwitz number. Finally we relate the topological types of generic real meromorphic functions with monodromy of orbifold coverings.