Milnor open books and Milnor fillable contact 3-manifolds
By C. Caubel, A. Némethi, Patrick Popescu‐Pampu. 2004
87 citations recorded by the source corpus.
We say that an oriented contact manifold (M,?) is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity . 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 , with isolated singularity at x and we verify that all these open books carry the contact structure ? of (M,?)?generalizing results of Milnor and Giroux.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/73fcede0ce87d8ff02d4d27f2556099f55c6d85b
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In Geometry and Topology
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- Mark McLean
- A. Stipsicz
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Citations in the corpus
- Reeb orbits and the minimal discrepancy of an isolated singularity (2014, background): “In fact every oriented three manifold admits at most one Milnor fillable contact structure up to orientation preserving diffeomorphism [CNPP06].”
- The diffeomorphism type of symplectic fillings (2016, background): “(In [5], that name refers to the singular filling.”