Constructions of generalized complex structures in dimension four

Abstract

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-manifolds, both simply and non-simply connected, which are neither complex nor symplectic.