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

Abstract

The link of a real analytic map germ f:(R3,0)→(R3,0) is obtained by taking the intersection of the image with a small enough sphere S2ϵ centered at the origin in R3. If ff is finitely determined, then the link is a stable map γγ from S2 to S2. We define Gauss words which contains all the topological information of the link in the case that the singular set S(γ) is connected and we prove that in this case they provide us with a complete topological invariant.