Construcción de aplicaciones estables de $3$-variedades en $\mathbb{R}^3$

Nelson Berrocal Huamani; Catarina  Mendes de Jesus  Sánchez

doi:10.5269/bspm.52610

Nelson Berrocal Huamani Universidad Nacional de San Crist´obal de Huamanga https://orcid.org/0000-0001-8554-3503
Catarina Mendes de Jesus Sánchez Universidad Federal de Juiz de Fora https://orcid.org/0000-0002-1050-2712

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.

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References

V. V. Goryunov, Local invariants of maps between 3-manifolds. J. Topol. 1-20, (2013) https://doi.org/10.1112/jtopol/jtt015 DOI: https://doi.org/10.1112/jtopol/jtt015

C. G. Gibson, Singular Points of Smooth Mappings. Reasearch Notes in Mathematics, Pitman, London, (1978).

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 DOI: https://doi.org/10.1016/j.topol.2006.04.005

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 DOI: https://doi.org/10.1201/9780203912089.ch10

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).

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 DOI: https://doi.org/10.1007/s00574-019-00133-4

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 DOI: https://doi.org/10.1007/BFb0066824

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 DOI: https://doi.org/10.1017/S030500410007434X

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 DOI: https://doi.org/10.1134/S0081543809040178

R. Oset Sinha, Topological invariants of stable maps from 3-manifolds to three-space, Proc. Liverpool SingularitiesSympos. Pg. 69 Valencia, (2009).

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 DOI: https://doi.org/10.1007/s00009-012-0224-2

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 DOI: https://doi.org/10.2307/1970070