### Abstract

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.

Original language | English |
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Pages (from-to) | 83-104 |

Number of pages | 22 |

Journal | Annales de l'Institut Fourier |

Volume | 66 |

Issue number | 1 |

Publication status | Published - Jan 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Annales de l'Institut Fourier*,

*66*(1), 83-104.