Stable Bi-Maps on Surfaces and Their Graphs
DOI:
https://doi.org/10.5540/tcam.2023.024.02.00337Keywords:
Stable maps, $\mathcal{RM}$-graphs, closed surfacesAbstract
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.
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