New Open-book Decompositions in Singularity Theory

Details New Open-book Decompositions in Singularity Theory New Open-book Decompositions in Singularity Theory

2010-06-03

arxiv.org/abs/1006.0600v2

Mathematics

Algebraic Geometry

25 pages, 10 figures; added reference for section 4

Scientific paper

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 $p,q,r \in \N$, $p,q,r \geq 2$ and $(p,q)=1$. Such a germ gives rise to a Milnor fibration $\frac{F}{\mid F \mid} \colon \Sp^5\setminus L_F \to \Sp^1$. 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 $\C^3$.

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