New examples of Neuwirth-Stallings pairs and non-trivial real Milnor fibrations

Author(s)

Maria Amelia de Pinho Barbosa Hohlenwerger

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2014-11-20

Examining board members

Raimundo Nonato Araújo dos Santos; Michelle Ferreira Zanchetta Morgado; Osamu Saeki; Marcelo José Saia; João Nivaldo Tomazella

• Advisor: Raimundo Nonato Araújo dos Santos

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. (AU)

• FAPESP's process: 12/12972-4 - Topology of real Milnor fiber
• Grantee: Maria Amelia de Pinho Barbosa Hohlenwerger
• Support Opportunities: Scholarships in Brazil - Doctorate