Caubel, Clément; Némethi, András; Popescu-Pampu, Patrick Milnor open books and Milnor fillable contact 3-manifolds. (English) Zbl 1098.53064 Topology 45, No. 3, 673-689 (2006). A construction of A. N. Varchenko [Mosc. Univ. Math. Bull. 35, No. 2, 18–22 (1980); translation from Vestn. Mosk. Univ., Ser. I 1980, No. 2, 18–21 (1980; Zbl 0453.53027)] associates with an irreducible germ \((X,x)\) of a complex analytic variety, which is smooth outside \(x\), an oriented real compact contact manifold; such a contact manifold is called Milnor fillable. The main theorem of the paper asserts that any Milnor fillable 3-manifold admits a unique Milnor fillable contact structure up to isomorphy. The proof is based on the connection between the Milnor fillable contact structures and the so-called open book decompositions. Reviewer: A. L. Onishchik (Yaroslavl) Cited in 3 ReviewsCited in 27 Documents MSC: 53D35 Global theory of symplectic and contact manifolds 32S55 Milnor fibration; relations with knot theory 57R17 Symplectic and contact topology in high or arbitrary dimension Keywords:contact structure; open book decomposition; isolated singularity Citations:Zbl 0453.53027 PDF BibTeX XML Cite \textit{C. Caubel} et al., Topology 45, No. 3, 673--689 (2006; Zbl 1098.53064) Full Text: DOI arXiv OpenURL