The paper focusses on the existence of higher open book structures defined by real map germs ψ :A general existence criterion is proved, with view to weighted-homogeneous maps.Keywords Real singularities · Milnor fibration · Links · Open book decompositions · Stratifications Mathematics Subject Classification (2000) 32S55 · 57Q45 · 32C40 · 32S60
IntroductionLet ψ : (R m , 0) → (R p , 0) be a non-trivial real analytic map germ. Let V := {ψ = 0} denote the germ at 0 of the zero locus of ψ, let B m ε ⊂ R m be the open ball of radius ε at the origin, let S m−1 ε := ∂ B ε and K ε := V ∩ S m−1 ε . Milnor studied in [11, §11] the setting Sing ψ ⊂ {0}, which means that the singular locus of the map germ ψ consists of at most the origin 0 ∈ R m . He shows in [11, p. 97-99] that for any small enough ε > 0, there is a smooth fiber bundle:
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