Milnor open books and Milnor fillable contact 3-manifolds. (English) Zbl 1098.53064

Caubel, Clément; Némethi, András; Popescu-Pampu, Patrick

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)

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