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

Raimundo Araújo Dos Santos, Maria A.B. Hohlenwerger, Osamu Saeki, Taciana O. Souza

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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 languageEnglish
Pages (from-to)83-104
Number of pages22
JournalAnnales de l'Institut Fourier
Volume66
Issue number1
Publication statusPublished - Jan 1 2016

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Dos Santos, R. A., Hohlenwerger, M. A. B., Saeki, O., & Souza, T. O. (2016). New examples of neuwirth-stallings pairs and non-trivial real milnor fibrations. Annales de l'Institut Fourier, 66(1), 83-104.