Stable Bi-Maps on Surfaces and Their Graphs - Mendes de Jesus, C.; Boizan Batista, E.; F. Costa, J. C. (Trends in Computational and Applied Mathematics, 2023)
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 and f1: M→R, f2: M→R^2 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.