Stable Bi-Maps on Surfaces and Their Graphs - Mendes De Jesus, C.; Boizan Batista, E.; Costa, J. C. F. [UNESP] (Sociedade Brasileira de Matemática Aplicada e Computacional - SBMAC, 2023)
In this paper we study stable bi-maps F=(f1,f2):M→ℝ×ℝ2 from a global viewpoint, where M is a smooth closed orientable surface and f1:M→ℝ,f2:M→ℝ2 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