Vector Bundles on Symplectic 4-Manifolds

Abstract

This thesis is an exposition on the relationship between symplectic manifolds, Kahler manifolds, and almost-complex manifolds using the theory of vector bundles and characteristic classes. This includes an introduction to the theory of fiber bundles and symplectic topology. These tools are used to construct the symplectic sum of [Gompf, 1995], and it culminates in a proof that all finitely presented groups can be realized as the fundamental group of a connected compact four-dimensional symplectic manifold. The material in this thesis is standard, but it is presented in a uniquely homotopy-theoretic manner whenever possible.