Sobre o teorema da fibração de Lê-Milnor e a topologia da fibra

Abstract

The main goal of this work is to show the Lê-Milnor local fibration theorem and to give some algebraic and topological characterizations for the Milnor number μ. The main result states that μ is equal to the Betti number of fiber in middle dimension. We approach the classic case of the fibration theorem studied by J. Milnor and the generalization presented by Lê D.T., for the case of germs of analytic functions defined in the singular complex analytic set X, the most general case being the one in which we consider f (X,0)→(C,0) function analytic with possibly non-isolated singularity at 0. Furthermore, we discuss some results concerning the topology of the fibrations in the sphere and in the "Milnor tube". To facilitate the understanding of the more general theory, we chose to present solved examples throughout certain chapters.