New Open-book Decompositions in Singularity Theory

Abstract

In this article, we study the topology of real analytic germs $F \colon (\C^3,0) \to (\C,0)$ 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 gives rise to a Milnor fibration $\frac{F}{\mid F \mid} \colon \Sp^5\setminus L_F \to \Sp^1$. We describe the link $L_F$ as a Seifert manifold and we show that in many cases the open-book decomposition of $\Sp^5$ given by the Milnor fibration of $F$ cannot come from the Milnor fibration of a complex singularity in $\C^3$.

25 pages, 10 figures; added reference for section 4

Cited by in corpus (3)

• The topology of real suspension singularities of type $f\bar{g}+z^n$
• Cyclic branched covers of knots as links of real isolated singularities
• Open book decompositions of ${\mathbb{S}}^5$ and real singularities