New Open-book Decompositions in Singularity Theory

2010/06/30 by Haydee Aguilar-Cabrera · 1 citation
Mathematics · #math.AG #msc:32S55 #msc:32S25 #msc:57M27

paper · pdf · doi:10.1007/s10711-011-9622-z

published as Geometriae Dedicata: Volume 158, Issue 1 (2012), Page 87-108 · 25 pages, 10 figures; added reference for section 4

arxiv created 2010/08/16 · arxiv updated 2012/11/22

Abstract

In this article, we study the topology 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 gives rise to a Milnor fibration (F)/(| F |) \colon \Sp⁵∖ L_F → \Sp¹. We describe the link L_F as a Seifert manifold and we show that in many cases the open-book decomposition of \Sp⁵ given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in \C³.

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