Introduction

Abstract

Abstract Symplectic topology is the study of the global phenomenon of symplectic geometry. In contrast the local structure of a symplectic manifold is, by Darboux’s theorem, always equivalent to the standard structure on Euclidean space. Hence there cannot be any local invariants in symplectic geometry. This should be contrasted with Riemannian geometry where the curvature provides such local invariants. These local invariants severely restrict the group of isometries and give rise to an infinite dimensional variety of nonequivalent Riemannian metrics. In symplectic geometry the absence of local invariants gives rise to an infinite dimensional group of diffeomor- phisms which preserve the symplectic structure and to a discrete set of nonequivalent global symplectic structures in each cohomology class.