 
Summary: HOLOMORPHIC OPEN BOOK DECOMPOSITIONS
CASIM ABBAS
Abstract. Emmanuel Giroux showed that every contact structure on a closed
three dimensional manifold is supported by an open book decomposition. We
will extend this result by showing that the open book decomposition can be
chosen in such a way that the pages are solutions to a homological perturbed
holomorphic curve equation.
Contents
1. Introduction 1
2. Existence and local foliations 7
2.1. Local model near the binding orbits 7
2.2. Functional Analytic setup and the Implicit Function Theorem 16
3. From local foliations to global ones 19
3.1. The Beltrami equation 24
3.2. A uniform L2
bound for the harmonic forms and uniform convergence 29
3.3. A uniform Lp
bound for the gradient 32
3.4. Convergence in W1,p
(B
