Gauss words and the topology of map germs from R-3 to R-3

摘要

The link of a real analytic map germ f: (R-3, 0) -> (R-3, 0) is obtained by taking the intersection of the image with a small enough sphere S-epsilon(2) centered at the origin in 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.