Milnor open books and Milnor fillable contact 3-manifolds

Details Milnor open books and Milnor fillable contact 3-manifolds Milnor open books and Milnor fillable contact 3-manifolds

2004-09-09

arxiv.org/abs/math/0409160v2

Topology 45 (2006), 673-689

Mathematics

Symplectic Geometry

17 pages

Scientific paper

We say that a contact manifold is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). Generalizing results of Milnor and Giroux, we associate to each holomorphic function f defined on X, with isolated singularity at x, an open book which supports the contact structure. Moreover, we prove that any 3-dimensional oriented manifold admits at most one Milnor fillable contact structure up to contactomorphism. * * * * * * * * In the first version of the paper, we showed that the open book associated to f carries the contact structure only up to an isotopy. Here we drop this restriction. Following a suggestion of Janos Kollar, we also give a simplified proof of the algebro-geometrical theorem 4.1, central for the uniqueness result.

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