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.
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 -