Topology of Fold Map Germs from R3 to R5

Let f : ( R 3 , 0 ) → ( R 5 , 0 ) be an analytic map germ with isolated instability. Its link is a stable map which is obtained by taking the intersection of the image of f with a small enough sphere S ϵ 4 centered at the origin in R 5 . If f is of fold type, we define a labeled tree associated to its link and prove that is a complete topological invariant for it. As an application we obtain the complete topological classification of map germs contained in the A 2 -class ( x , y , z 2 , x z , 0 ) .