Geometriae Dedicata

, Volume 158, Issue 1, pp 87–108 | Cite as

New open-book decompositions in singularity theory

Original Paper


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 \({\mathbb{C}^3}\).


Milnor fibration Real singularities Open-book decompositions Seifert manifolds 

Mathematics Subject Classification (2000)

32S55 32S25 57M27 


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Instituto de MatemáticasUnidad Cuernavaca, Universidad Nacional Autónoma de MéxicoCuernavacaMéxico
  2. 2.Institut de Mathématiques de LuminyUniversité de la MéditerranéeMarseilleFrance

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