Open book decompositions and stable Hamiltonian structures

Details Open book decompositions and stable Hamiltonian structures Open book decompositions and stable Hamiltonian structures

2008-08-24

arxiv.org/abs/0808.3220v3

Mathematics

Symplectic Geometry

13 pages, 2 figures; v3 includes some added details on implicit function theorems for punctured pseudoholomorphic curves; to a

Scientific paper

We show that every open book decomposition of a contact 3-manifold can be represented (up to isotopy) by a smooth R-invariant family of pseudoholomorphic curves on its symplectization with respect to a suitable stable Hamiltonian structure. In the planar case, this family survives small perturbations, and thus gives a concrete construction of a stable finite energy foliation that has been used in various applications to planar contact manifolds, including the Weinstein conjecture and equivalence of strong and Stein fillability.

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