Batista, Erica BoizanCosta, Joaõ Carlos Ferreira [UNESP]Nunõ-Ballesteros, Juan J.2018-12-112018-12-112017-05-01Proceedings of the Edinburgh Mathematical Society, v. 60, n. 2, p. 319-348, 2017.0013-0915http://hdl.handle.net/11449/173756We consider finitely determined map germs f : (ℝ3, 0) → (ℝ2, 0) with f -1(0) = {0} and we look at the classification of this kind of germ with respect to topological equivalence. By Fukuda's cone structure theorem, the topological type of f can be determined by the topological type of its associated link, which is a stable map from S 2 to S 1. We define a generalized version of the Reeb graph for stable maps γ : S 2 → S 1, which turns out to be a complete topological invariant. If f has corank 1, then f can be seen as a stabilization of a function h0: (ℝ2, 0) → (ℝ, 0), and we show that the Reeb graph is the sum of the partial trees of the positive and negative stabilizations of h 0. Finally, we apply this to give a complete topological description of all map germs with Boardman symbol Σ 2, 1.319-348engclassificationlinkReeb graphtopological equivalenceArtigo10.1017/S0013091516000274Acesso aberto2-s2.0-849946272082-s2.0-84994627208.pdf