Revista Matemática Iberoamericana


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Volume 31, Issue 3, 2015, pp. 977–988
DOI: 10.4171/RMI/860

Published online: 2015-10-29

Gauss words and the topology of map germs from $\mathbb R^3$ to $\mathbb R^3$

Juan Antonio Moya-Pérez[1] and Juan José Nuño Ballesteros[2]

(1) Universitat de València, Burjassot (Valencia), Spain
(2) Universitat de València, Burjassot (Valencia), Spain

The link of a real analytic map germ $f\colon (\mathbb{R}^{3}, 0) \to (\mathbb{R}^{3}, 0)$ is obtained by taking the intersection of the image with a small enough sphere $S^2_\epsilon$ centered at the origin in $\mathbb R^3$. If $f$ is finitely determined, then the link is a stable map $\gamma$ from $S^2$ to $S^2$. We define Gauss words which contains all the topological information of the link in the case that the singular set $S(\gamma)$ is connected and we prove that in this case they provide us with a complete topological invariant.

Keywords: Gauss word, link, finite determinacy

Moya-Pérez Juan Antonio, Nuño Ballesteros Juan José: Gauss words and the topology of map germs from $\mathbb R^3$ to $\mathbb R^3$. Rev. Mat. Iberoam. 31 (2015), 977-988. doi: 10.4171/RMI/860