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 : (R 3 , 0) → (R 3 , 0) is obtained by taking the intersection of the image with a small enough sphere S 2 centered at the origin in R 3 . If f is finitely determined, then the link is a stable map γ 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(γ) is connected and we prove that in this case they provide us with a complete topological invariant.

The dual tree of a fold map germ from to

“…Finally, let us remark that the techniques used in this paper of obtaining the topological classification of real analytic map germs by means of its associated link has been used by both authors and the second author with several collaborators in other cases [1,2,[15][16][17]18].…”

The Reeb Graph of a Map Germ from ℝ3 to ℝ2 with Isolated Zeros

“…The topological classification of map germs with non-isolated zeros will be considered in a forthcoming paper [2]. Some recent papers treat the topological classification of finitely determined map germs f : (R n , 0) → (R p , 0) by looking at the topological type of the link (see, for instance, [3,11,[14][15][16]). However, as far as we know, this is the first time that it is considered for the n > p case.…”