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

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.