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

### Juan Antonio Moya-Pérez

Universitat de València, Burjassot (Valencia), Spain### Juan José Nuño Ballesteros

Universitat de València, Burjassot (Valencia), Spain

## Abstract

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.

## Cite this article

Juan Antonio Moya-Pérez, Juan José Nuño Ballesteros, Gauss words and the topology of map germs from $\mathbb R^3$ to $\mathbb R^3$. Rev. Mat. Iberoam. 31 (2015), no. 3, pp. 977–988

DOI 10.4171/RMI/860