Stable bi-maps from closed orientable surfaces to R x R

Abstract

In this paper we study stable bi-maps f = (f1, f2) : M → R × R 2 from a global viewpoint, where M is a smooth closed orientable surface. We associate a bi-graph to f , so-called RM-graph and study their properties. In this work we are looking for realization conditions for RM-graphs associated to stable bi-maps.