Generic Geometry of Stable Maps of 3-Manifolds into R4

We describe the generic geometry of the 3 D -crosscap (image of a stable map of a 3-manifold into R 4 ) by means of the simultaneous analysis of the generic singularities of height and squared distanced functions on the flag composed by the 3-manifold, the surface of double points and the crosscaps...

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Bibliographic Details
Published in:Boletim da Sociedade Brasileira de Matemática 2021, Vol.52 (3), p.547-561
Main Authors: Casonatto, C., Fuster, M. C. Romero, Atique, R. Wik
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Singularity (mathematics)
Theoretical
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Summary:We describe the generic geometry of the 3 D -crosscap (image of a stable map of a 3-manifold into R 4 ) by means of the simultaneous analysis of the generic singularities of height and squared distanced functions on the flag composed by the 3-manifold, the surface of double points and the crosscaps curve at any point of this curve.
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-020-00217-6