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In this work, we focus on the study of the topology of the Milnor fibration associated with a polynomial map germ f : (R, 0) → (R, 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 (S, K), 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 (R, 0) → (R, 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.

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