Poisson Manifolds and Holomorphic Curves

Abstract

In this thesis we study the topology of Poisson manifolds using techniques from symplectic topology, especially holomorphic curves. In particular, we study the topology of regular Poisson manifolds (symplectic foliations), log-symplectic manifolds, and scattering-symplectic manifolds. The first two are examined by looking at certain spaces of holomorphic curves, the last by relating it to a composition of symplectic cobordisms between contact manifolds. As applications we find several obstructions to the existence of such Poisson structures on certain manifolds. Moreover, with the same tools we prove a classification result for ruled 4-dimensional log-symplectic manifolds.