Gauss words and the topology of map germs from \(\mathbb{R}^3\) to \(\mathbb{R}^3\)
type: Item
instance of: scholarly article
title: Gauss words and the topology of map germs from \(\mathbb{R}^3\) to \(\mathbb{R}^3\)
zbMATH Open document ID: 1335.58024
DOI: 10.4171/RMI/860
author: Juan Antonio Moya-Pérez
author: J. J. Nuño-Ballesteros
published in: Revista Matemática Iberoamericana
publication date: 2015-11-03T00:00:00Z
review text: The topological structure of a real-analytic, finitely determined, map germ \(f:({\mathbb R}^3,0)\to ({\mathbb R}^3,0)\) is determined by the link of \(f\), which, according to a theorem of \textit{T. Fukuda} [Invent. Math. 65, 227--250 (1981; Zbl 0499.58008)], is a stable map \(\gamma\) from \({\mathbb S}^2\) to \({\mathbb S}^2\). The authors define an adapted version of Gauss words which contain all the topological information of the link when the singular set \(S(\gamma)\) is connected. In this case, they show that the Gauss words provide a complete topological invariant.
reviewed by: Vincent Thilliez
Mathematics Subject Classification ID: 58K15
Mathematics Subject Classification ID: 58K40
Mathematics Subject Classification ID: 58K60
zbMATH DE Number: 6503644
zbMATH Keywords: Gauss words
zbMATH Keywords: link
zbMATH Keywords: finite determinacy
MaRDI profile type: Publication
cites work: Stable maps between 2-spheres with a connected fold curve
cites work: Local topological properties of differentiable mappings. I
cites work: Q3862121
cites work: Fold Maps from the Sphere to the Plane
cites work: The doodle of a finitely determined map germ from \(\mathbb R^2\) to \(\mathbb R^3\)
cites work: Finitely determined singularities of ruled surfaces in 3
cites work: Singular Points of Complex Hypersurfaces. (AM-61)
cites work: The link of a finitely determined map germ from \(R^{2}\) to \(R^{2}\)
cites work: Topological classification of corank 1 map germs from \(\mathbb R^3\) to \(\mathbb R^3\)
cites work: Q4848735
cites work: Finite Determinacy of Smooth Map-Germs
cites work: Equivalence of stable mappings between two-dimensional manifolds
full work available at URL: https://doi.org/10.4171/rmi/860
OpenAlex ID: W2495963642
description: scientific article; zbMATH DE number 6503644