TY - JOUR

T1 - New examples of neuwirth-stallings pairs and non-trivial real milnor fibrations

AU - Dos Santos, Raimundo Araújo

AU - Hohlenwerger, Maria A.B.

AU - Saeki, Osamu

AU - Souza, Taciana O.

N1 - Publisher Copyright:
© Association des Annales de l'institut Fourier, 2016, Certains droits réservés.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2016

Y1 - 2016

N2 - We use the topology of configuration spaces to give a characterization of Neuwirth-Stallings pairs (S5,K) with dimK = 2. As a consequence, we construct polynomial map germs (R6, 0) → (R3, 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 (R2n, 0) → (Rn, 0) or (R2n+1, 0) → (Rn, 0), n 7ge; 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 (Rn, 0) → (Rp, 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.

AB - We use the topology of configuration spaces to give a characterization of Neuwirth-Stallings pairs (S5,K) with dimK = 2. As a consequence, we construct polynomial map germs (R6, 0) → (R3, 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 (R2n, 0) → (Rn, 0) or (R2n+1, 0) → (Rn, 0), n 7ge; 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 (Rn, 0) → (Rp, 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.

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U2 - 10.5802/aif.3006

DO - 10.5802/aif.3006

M3 - Article

AN - SCOPUS:84960906956

VL - 66

SP - 83

EP - 104

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

SN - 0373-0956

IS - 1

ER -