Open book decompositions and stable Hamiltonian structures

Abstract

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 (Abbas et al., 2005) [2] and the equivalence of strong and Stein fillability (Wendl, to appear) [20].