Holomorphic Curves in Symplectic Cobordisms

Abstract

In this chapter, the focus shifts from closed symplectic 4-manifolds to contact 3-manifolds and symplectic cobordisms between them, starting from a historical overview of the conjectures of Arnold and Weinstein, and leading into the development of Floer homology and symplectic field theory. We then give an overview of useful technical results on punctured holomorphic curves in cobordisms; as in Chap. 2, the focus here is on precise statements rather than proofs, though heuristic explanations are sometimes given.