Stable Bi-Maps on Surfaces and Their Graphs

C. Mendes de Jesus, E. Boizan Batista, J. C. F. Costa


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.


Stable maps, $\mathcal{RM}$-graphs, closed surfaces

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