Open book decompositions of ${\mathbb{S}}^5$ and real singularities

Abstract

In this article, we study the topology of the family of real analytic germs $F:({\mathbb{C}}^3,0)\to (\mathbb{C},0)$ given by $F(x,y,z)=\overline{xy}(x^p+y^q)+z^r$ with $p,q,r\in \mathbb{N}$, $p,q,r\ge 2$ and $(p,q)=1$. Such a germ has isolated singularity at 0 and gives rise to a Milnor fibration $\frac{F}{|F|}:{\mathbb{S}}^5\setminus L_F\to {\mathbb{S}}^1$. We describe the link $L_F$ 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 ${\mathbb{S}}^5$ given by the Milnor fibration of $F$ cannot come from the Milnor fibration of a complex singularity in ${\mathbb{C}}^3$.

20 pages. arXiv admin note: text overlap with arXiv:1006.0600

References in corpus (3)

• Complete intersection singularities of splice type as universal abelian covers
• Complex surface singularities with integral homology sphere links
• New Open-book Decompositions in Singularity Theory