| Full text | |
| Author(s): |
dos Santos, Raimundo Araujo
;
Hohlenwerger, Maria A. B.
;
Saeki, Osamu
;
Souza, Taciana O.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | ANNALES DE L INSTITUT FOURIER; v. 66, n. 1, p. 83-104, 2016. |
| Web of Science Citations: | 2 |
| Abstract | |
We use the topology of configuration spaces to give a characterization of Neuwirth-Stallings pairs (S-5, K) with dim K = 2. As a consequence, we construct polynomial map germs (R-6, 0) -> (R-3, 0) with an isolated singularity at the origin such that their Milnor fibers are not diffeomorphic to a disk, thus putting an end to Milnor's non-triviality question. Furthermore, for a polynomial map germ (R-2n, 0) -> (R-n, 0) or (R2n+1 , 0) -> (R-n, 0) n >= 3, with an isolated singularity at the origin, we study the conditions under which the associated Milnor fiber has the homotopy type of a bouquet of spheres. We then construct, for every pair (n, p) with n/2 >= p >= 2, a new example of a polynomial map germ (R-n, 0) -> (R-P, 0) with an isolated singularity at the origin such that its Milnor fiber 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 |
| FAPESP's process: | 13/23443-5 - Topology of the fibers of real and complex polynomials mappings: local and global (at infinity) aspects |
| Grantee: | Raimundo Nonato Araújo dos Santos |
| Support Opportunities: | Regular Research Grants |