Generic Geometry of Stable Maps of 3-Manifolds into \({\mathbb {R}}^4\)

Abstract

We describe the generic geometry of the 3D-crosscap (image of a stable map of a 3-manifold into \(\mathbb {R}^4\)) 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.

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Funding

M. C. Romero Fuster: MINECO/FEDER (MTM2015-64013-P) R. Wik Atique: Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP (2015/04409-6).

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Correspondence to C. Casonatto.

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Casonatto, C., Fuster, M.C.R. & Atique, R.W. Generic Geometry of Stable Maps of 3-Manifolds into \({\mathbb {R}}^4\). Bull Braz Math Soc, New Series (2020). https://doi.org/10.1007/s00574-020-00217-6

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Keywords

  • Singularities
  • Flat geometry
  • 3D-crosscap
  • Contacts

Mathematics Subject Classification

  • 57R45
  • 53A07