Contact 3-Manifolds and Symplectic Fillings

Abstract

This chapter sketches some applications of the punctured holomorphic curve machinery from Chap. 8 to problems in three-dimensional contact topology, including the Weinstein conjecture and the question of symplectic fillability. It concludes with a discussion of open book decompositions, the special role played by planar contact manifolds, and the theorem that fillings of the latter always arise from Lefschetz fibrations.