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New open-book decompositions in singularity theory
Authors:Haydée Aguilar-Cabrera
Institution:1. Instituto de Matem??ticas, Unidad Cuernavaca, Universidad Nacional Aut??noma de M??xico, Cuernavaca, M??xico
2. Institut de Math??matiques de Luminy, Universit?? de la M??diterran??e, Marseille, France
Abstract:In this article, we study the topology of real analytic germs ${F \colon (\mathbb{C}^3,0) \to (\mathbb{C},0)}$ given by ${F(x,y,z)=\overline{xy}(x^p+y^q)+z^r}$ with ${p,q,r \in \mathbb{N}, p,q,r \geq 2}$ and (p, q)?=?1. Such a germ gives rise to a Milnor fibration ${\frac{F}{\mid F \mid}\colon \mathbb{S}^5\setminus L_F \to \mathbb{S}^1}$ . We describe the link L F as a Seifert manifold and we show that in many cases the open-book decomposition of ${\mathbb{S}^5}$ given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in ${\mathbb{C}^3}$ .
Keywords:
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