Milnor open books and Milnor fillable contact 3-manifolds |
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Authors: | Clément Caubel Patrick Popescu-Pampu |
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Institution: | a Univ. Paris 7 Denis Diderot, Inst. de Maths.—UMR CNRS 7586, Équipe “Géométrie et Dynamique” Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France b Rényi Institute of Mathematics, P.O.B. 127, H-1364 Budapest, Hungary |
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Abstract: | We say that an oriented contact manifold (M,ξ) is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). In this article we prove that any three-dimensional oriented manifold admits at most one Milnor fillable contact structure up to contactomorphism. The proof is based on Milnor open books: we associate an open book decomposition of M with any holomorphic function f:(X,x)→(C,0), with isolated singularity at x and we verify that all these open books carry the contact structure ξ of (M,ξ)—generalizing results of Milnor and Giroux. |
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Keywords: | 32S55 53D10 32S25 57R17 |
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