Topological K-classification of finitely determined map germs

Abstract

We consider smooth finitely C 0-K-determined map germs f: (ℝn, 0) → (ℝp, 0) and we look at the classification under C 0-K-equivalence. The main tool is the homotopy type of the link, which is obtained by intersecting the image of f with a small enough sphere centered at the origin. When f -1(0) = {0}, the link is a smooth map between spheres and f is C 0-K-equivalent to the cone of its link. When f -1(0) ≠ {0}, we consider a link diagram, which contains some extra information, but again f is C 0-K-equivalent to the generalized cone. As a consequence, we deduce some known results due to Nishimura (for n = p) or the first named author (for n < p). We also prove some new results of the same nature. © 2012 Springer Science+Business Media Dordrecht.