Novos exemplos de NS-pares e de fibrações de Milnor reais não-triviais

Abstract

In this work, we focus on the study of the topology of the Milnor fibration associated with a polynomial map germ f : (Rn; 0) ! (Rp; 0) with an isolated singularity at the origin. The first result is an extension of the characterization of trivial map germs in the pairs of dimensions (n; p) when n 􀀀 p = 3: An initial characterization was presented by Church and Lamotke in 1975. The second result is a characterization of NS-pairs (S5;K2); using the topology of configuration spaces. As a consequence of this characterization, we show the existence of real polynomial map germs in the pairs of dimensions (6; 3) with an isolated singularity at the origin such that its Milnor fibers are not diffeomorphic to a disc. The existence of such examples ends a non-triviality problem posed by Milnor in 1968 and furthermore, it allows us to show a new result about the topology of the real Milnor fibers in the pairs of dimensions (2n; n) and (2n + 1; n); n > 3: This result ensure the existence of polynomial map germs (Rn; 0) ! (Rp; 0); n > p > 2; with an isolated singularity at the origin such that its Milnor fibers has the homotopy type of a bouquet of a positive number of spheres.