Generic geometry of stable maps of 3-manifolds into \(\mathbb{R}^4\)
type: Item
instance of: scholarly article
title: Generic geometry of stable maps of 3-manifolds into \(\mathbb{R}^4\)
zbMATH Open document ID: 1486.57040
author: C. Casonatto
author: Carmen Romero-Fuster
author: R. G. Wik Atique
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2021-07-28T00:00:00Z
review text: In this paper, the authors study the generic geometry of the 3D-crosscap, image of a germ in the \(\mathcal{A}\)-orbit of \((x, y,z^2, yz)\), by means of the simultaneous analysis of the generic singularities of height and squared distance functions on the flag composed by the 3-manifold, the surface of double points and the crosscaps curve at any point of this curve. They use the same approach as in [\textit{J. W. Bruce} and \textit{J. M. West}, Math. Proc. Camb. Philos. Soc. 123, No. 1, 19--39 (1998; Zbl 1006.53005)] in order to study the geometry of the image of a stable map from a 3-manifold to \(\mathbb R^4\). They obtain all the possible geometrical phenomena and their interpretation given by contacts with hyperplanes and hyperspheres occurring at a generic point of a 3D-crosscap, as well as those concerning contacts with hyperplanes occurring in generic 1-parameter families of stable maps from a 3-manifold to \(\mathbb{R}^4\).
reviewed by: Pedro Benedini Riul
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 7375727
zbMATH Keywords: singularities
zbMATH Keywords: flat geometry
zbMATH Keywords: 3D-crosscap
zbMATH Keywords: contacts
MaRDI profile type: Publication
full work available at URL: s00574-020-00217-6
OpenAlex ID: W3037519050
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DOI: 10.1007/S00574-020-00217-6
description: scientific article; zbMATH DE number 7375727