Abstract
This paper presents some graphs with weights, associated with the maps of $3$-varieties in $\mathbb{R}^3$, and a scheme using these graphs for the construction of these stable applications of $S^3$, $S^1 \times S^2$ and the related sum between them in $\mathbb{R}^3$, with a predetermined singular set, making use of surgeries between maps. In addition to studying the relationship between graphs and stable maps.
Publisher
Sociedade Paranaense de Matematica
Reference12 articles.
1. V. V. Goryunov, Local invariants of maps between 3-manifolds. J. Topol. 1-20, (2013) https://doi.org/10.1112/jtopol/jtt015
2. C. G. Gibson, Singular Points of Smooth Mappings. Reasearch Notes in Mathematics, Pitman, London, (1978).
3. D. Hacon, C. Mendes de Jesus and M. C. Romero Fuster, Stable maps from surfaces to the plane with prescribed branching data, Topology and Its Appl. 154, 166-175, (2007). https://doi.org/10.1016/j.topol.2006.04.005
4. D. Hacon, C. Mendes de Jesus and M. C. Romero Fuster, Topological invariants of stable maps from a surface to the plane from a global viewpoint, Real and Complex Singularities. (2003). https://doi.org/10.1201/9780203912089.ch10
5. N. B. Huamanı, Grafos associados 'as aplica¸c˜oes est'aveis de 3-variedades fechadas e orientadas no R 3 , Disserta¸c˜ao de Mestrado. (2016).