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REAL ANALYTIC GERMS AND OPEN-BOOK DECOMPOSITIONS OF THE 3-SPHERE

ANNE PICHON

Institut de Mathématiques de Luminy, UMR 6206 CNRS, Campus de Luminy — Case 907, 13288 Marseille Cedex 9, France

https://doi.org/10.1142/S0129167X05002710Cited by:24 (Source: Crossref)

Abstract

Let f,g: (C²,0) → (C,0) be two holomorphic germs with isolated singularities and no common branches and let L_f, be their links. We prove that the real analytic germ has an isolated singularity at 0 if and only if the link L_f ∪ -L_g is fibred. This was conjectured by Rudolph in [14]. If this condition holds, then the underlying Milnor fibration is an open-book fibration of the link L_f ∪ -L_g which coincides with in a tubular neighbourhood of this link. This enables one to realize a large family of fibrations of plumbing links in S³ as the Milnor fibrations of some real analytic germs .

Keywords:

AMSC: 14J17, 57M25

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