Open book decompositions of \mathbbS⁵ and real singularities

2013/05/14 by Haydée Aguilar-Cabrera, Aguilar-Cabrera, Haydée
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Primary 32S55 #Secondary 57M27 #math.AG #math.GT #msc:32S55 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1305.2983

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

arxiv created 2013/05/14 · arxiv updated 2013/05/15

Abstract

In this article, we study the topology of the family of real analytic germs F \colon (ℂ³,0) → (ℂ,0) given by F(x,y,z)=xy(x^p+y^q)+z^r with p,q,r ∈ ℕ, p,q,r ≥ 2 and (p,q)=1. Such a germ has isolated singularity at 0 and gives rise to a Milnor fibration (F)/(|F|) \colon \mathbbS⁵ ∖ L_F → \mathbbS¹. 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 \mathbbS⁵ given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in ℂ³.

Citations

• New Open-book Decompositions in Singularity Theory

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• A Note On Non-Isolated Real Singularities and Links