Open book decompositions of S⁵ and real singularities

الأصل · EN

In this article, we study the topology of the family of real analytic germs F (C³,0) → (C,0) given by F(x,y,z)=xy(xᵖ+yq)+zʳ with p,q,r ∈ N, p,q,r ≥ 2 and (p,q)=1. Such a germ has isolated singularity at 0 and gives rise to a Milnor fibration F/|F| S⁵ LF → S¹. We describe the link LF as a Seifert manifold and we show that it is always homeomorphic to the link of a complex singularity. However, we prove that in almost all the cases the open-book decomposition of S⁵ given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in C³.