Gauss words and the topology of map germs from \(\mathbb{R}^3\) to \(\mathbb{R}^3\)
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.
scientific article; zbMATH DE number 6503644