ABSTRACT
In this paper we study stable bi-maps from a global viewpoint, where M is a smooth closed orientable surface and are stable maps. We associate a graph to F, so-called ℛℳ-graph and study its properties. The ℛℳ-graph captures more information about the topological structure of M than other graphs that appear in literature. Moreover, some graph realization theorems are obtained.
Keywords:
Stable maps; ℛℳ-graphs; closed surfaces