Graphs: A global invariant of the stable maps

Alana Cavalcante Felippe, Catarina Mendes de Jesus Sanchez

Resumo


In Singularity theory, maps from closed surfaces to the 2−sphere have been much studied(see [1], [6], [7]). An important problem is to search of invariants for the classification of thestable maps. In [6], Ohmoto and Aicardi determined local invariants of stable maps betweensurfaces, from codimension one transition over the image of the map. [...]

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Referências


Demoto, S. Stable maps between 2-spheres with a connected fold curve,Hiroshima Math. J.35:93–113, 2005. DOI:10.32917/hmj/1150922487.

Hacon, D., Mendes de Jesus, C., and Romero Fuster, M.C. Topological invariants of stablemaps from a surface to the plane from a global viewpoint,Real and Complex Singularities.Informa UK Limited, 1:227–235, 2003. DOI:10.1201/9780203912089.ch10.

Hacon, D., Mendes de Jesus, C., and Romero Fuster, M.C. Stable maps from surfacesto the plane with prescribed branching data,Topology and Its Appl., 154:166–175, 2007.DOI:http://dx.doi.org/10.1016/j.topol.2006.04.005.

Hacon, D., Mendes de Jesus, C., and Romero Fuster, M.C. Graphs of stable maps from closedorientable surfaces to the 2-sphere,J. Sing., 2:67–80, 2010. DOI:10.5527/jsing.2010.2e.

Mendes de Jesus, C., and Romero Fuster, M.C. Graphs of stable maps from clo-sed surfaces to the projective plane,Topology and Its Appl., 234:298–310, 2018. DOI:https://doi.org/10.1016/j.topol.2017.11.013

Ohmoto, T., and Aicardi, F. First Order Local Invariants of Apparent Coutours,Topology,45: 27–45, 2006. DOI: 10.1016/j.top.2005.04.005.[7] Yamamoto, T. Apparent contours with minimal number of singularities.Kyushu J. Math,64:1–16, 2010. DOI: 10.2206/kyushujm.64.1


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