Stable bi-maps from closed orientable surfaces to R x R
DOI:
https://doi.org/10.5540/03.2021.008.01.0481Palabras clave:
Stable maps, RM-graphs, closed surfacesResumen
In this paper we study stable bi-maps f = (f1; f2) : M ! R x R2 from a global viewpoint, where M is a smooth closed orientable surface. We associate a bi-graph to f, so-called RM-graph and study their properties. In this work we are looking for realization conditions for RM-graphs associated to stable bi-maps.
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Arnold, V.I., Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem, Math. Phys. Anal. Geom., 10:227-236, 2007.
Batista, E.B., Costa, J.C.F., Nuno-Ballesteros, J.J., The Reeb graph of a map germ from R3 to R2 with isolated zeros, Proc. Edinb. Math. Soc., 60(2):319-348, 2016.
Batista, E.B., Costa, J.C.F., Nuno-Ballesteros, J.J., The Reeb graph of a map germ from R3 to R2 without isolated zeros, Bull. Brazilian Math. Soe., 49(2):369-394, 2018.
Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B., Reeb graphs for shape analysis and applications, Theoretical Computer Science, 392:5-22, 2008.
Hacon, D., Mendes de Jesus, C., Romero-Fuster, M.C., Topological invariants of stable maps from a surface to the plane from a global viewpoint, Proc. 6th Workshop on Real and Complex Singularities. Lecture Notes in Pure and Applied Mathematics, 232:227235, 2003.
Hacon, D., Mendes de Jesus, C., Romero-Fuster, M.C., Fold maps from the sphere to the plane, Experiment. Math. 15(4):491-497, 2006.
Hacon, D., Mendes de Jesus, C., Romero-Fuster, M.C., Stable maps from surfaces to the plane with prescribed branching data, Topology and its Appl., 154:166-175, 2007.
Hacon, D., Mendes de Jesus, C., Romero-Fuster, M.C., Graphs of stable maps from closed orientable surfaces to the 2-sphere, J. Singularities, 2:67-80, 2010.
Kudryavtseva, E.A., Realization of smooth functions on surfaces as height functions, Sb. Math., 190(3):349-405, 1999.
Mendes de Jesus, C., Romero-Fuster, M.C., Graphs of stable maps from closed surfaces to the projective plane, Topology and its Appl., 234:298-310, 2018.
Ohmoto, T., Aicardi, F., First order local invariants of apparent coutours, Topology, 45:27-45, 2006.
Reeb, G., Sur les points singuliers d’une forme de Pfaff completement intégrable ou d’une fonction numérique, C. R. Acad. Sci. Paris, 222:847-849, 1946.
Whitney, H., On singularities of mappings of Euclidean spaces. I. Mappings of the Plane into the Plane, Ann. of Math., 62:374-410, 1955.
