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.

References in corpus (2)

• Exotic smooth structures on 4-manifolds with zero signature
• Minimizing Euler characteristics of symplectic four-manifolds

Cited by in corpus (6)

• Stable generalized complex structures
• On the number of type change loci of a generalized complex structure
• Fibrations and stable generalized complex structures
• Fibrations in semi-toric and generalized complex geometry
• Odd type generalized complex structures on 4-manifolds
• Generalized Luttinger surgery and other cut-and-paste constructions in generalized complex geometry