A topologia da fibra de milnor-lê para funções de três variáveis reais

Abstract

In this work, we describe results relating to topology of the Milnor bration of function-germs in R³. Initially, we describe the topological type of Milnor ber inassociation to the conelike function-germ f : (R³, 0) → (R, 0) of class Cl, with l ≥ 1 and isolated critical value. Then, we extend for the real case the result due to Lê andTeissier to complex function-germs, in other words, we prove that the topological type of the ber does not depend on the choice of a suitable fundamental system of the neighborhoods of 0 in R³. We also describe the topological type of the Milnor ber Fg of the function ||g|| dened in a subanalitic 3-dimentional set X ⊂ R³ in terms of the embedded topological type of its link K g. Precisally, we prove that the interior of the Milnor ber of F g ishomeomorphic to the complement of K g in the sphere S²£.

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