The link of a finitely determined map germ from \(R^{2}\) to \(R^{2}\). (English) Zbl 1225.58018

Moya-Pérez, J. A.; Nuño-Ballesteros, J. J.

J. Math. Soc. Japan 62, No. 4, 1069-1092 (2010).

Let \(f:({\mathbb R}^2,0)\to ({\mathbb R}^2,0)\) be a real-analytic finitely determined map germ. The link of \(f\) is defined by the intersection of the image of \(f\) in a neighborhood of \(0\) with a sufficiently small sphere centered at \(0\).
The authors associate an adapted version of Gauss words with the link of \(f\), and they show that two finitely determined map germs are topologically equivalent if and only if they have equivalent Gauss words. Various classification results are derived.

Reviewer: Vincent Thilliez (Villeneuve d’Ascq)

MSC:

58K40	Classification; finite determinacy of map germs
58K15	Topological properties of mappings on manifolds
58K65	Topological invariants on manifolds

Keywords:

finitely determined map germs; real singularities; topological classification; link; Gauss word

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