Construcción de aplicaciones estables de $3$-variedades en $\mathbb{R}^3$
DOI:
https://doi.org/10.5269/bspm.52610Abstract
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.
References
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¸cËœoes est'aveis de 3-variedades fechadas e orientadas no R 3 , Disserta¸cËœao de Mestrado. (2016).
6. N. B. Huamanı, Mendes de Jesus C. and Palacios J, Invariants of stable maps from the 3-sphere to the Euclidean 3-space, Bull Braz Math Soc, New Series 50, 913 (2019). https://doi.org/10.1007/s00574-019-00133-4
7. J. N. Mather, Stability of C1 Mappings VI: The Nice Dimensions, Proc. Liverpool Singularities-Sympos. 92, 207-253, (1971). https://doi.org/10.1007/BFb0066824
8. W. Marar and F. Tari, On the geometry of simple germs of co-rank 1 maps from R 3 to R 3 , Math. Proc. Camb. Philos. Soc. 119(3), 469-481 (1996). https://doi.org/10.1017/S030500410007434X
9. C. Mendes de Jesus, R. Oset Sinha. and M. C. Romero Fuster, Global topological invariants of stable maps from 3-manifolds to R3 , Proceedings of the Steklov Institute of Mathematics. 267, 205-216, (2009). https://doi.org/10.1134/S0081543809040178
10. R. Oset Sinha, Topological invariants of stable maps from 3-manifolds to three-space, Proc. Liverpool SingularitiesSympos. Pg. 69 Valencia, (2009).
11. R. O. Sinha and M. C. Romero Fuster, Graphs of stable maps from 3-manifolds to 3-space. Mediterr. J. Math. 10, 1107-1126, (2013). https://doi.org/10.1007/s00009-012-0224-2
12. C. H. Whitney, On singularities of mappings of Euclidean spaces. I. mappings of the plane into the plane, Ann. of Math. 62, 374-410, (1955). https://doi.org/10.2307/1970070
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¸cËœoes est'aveis de 3-variedades fechadas e orientadas no R 3 , Disserta¸cËœao de Mestrado. (2016).
6. N. B. Huamanı, Mendes de Jesus C. and Palacios J, Invariants of stable maps from the 3-sphere to the Euclidean 3-space, Bull Braz Math Soc, New Series 50, 913 (2019). https://doi.org/10.1007/s00574-019-00133-4
7. J. N. Mather, Stability of C1 Mappings VI: The Nice Dimensions, Proc. Liverpool Singularities-Sympos. 92, 207-253, (1971). https://doi.org/10.1007/BFb0066824
8. W. Marar and F. Tari, On the geometry of simple germs of co-rank 1 maps from R 3 to R 3 , Math. Proc. Camb. Philos. Soc. 119(3), 469-481 (1996). https://doi.org/10.1017/S030500410007434X
9. C. Mendes de Jesus, R. Oset Sinha. and M. C. Romero Fuster, Global topological invariants of stable maps from 3-manifolds to R3 , Proceedings of the Steklov Institute of Mathematics. 267, 205-216, (2009). https://doi.org/10.1134/S0081543809040178
10. R. Oset Sinha, Topological invariants of stable maps from 3-manifolds to three-space, Proc. Liverpool SingularitiesSympos. Pg. 69 Valencia, (2009).
11. R. O. Sinha and M. C. Romero Fuster, Graphs of stable maps from 3-manifolds to 3-space. Mediterr. J. Math. 10, 1107-1126, (2013). https://doi.org/10.1007/s00009-012-0224-2
12. C. H. Whitney, On singularities of mappings of Euclidean spaces. I. mappings of the plane into the plane, Ann. of Math. 62, 374-410, (1955). https://doi.org/10.2307/1970070
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2022-12-21
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