Deformation of Generalized Complex Structures and Topological Sigma Models


We present the construction of a general type of topological sigma-model on generalized Calabi-Yau (GCY) manifolds, which includes the familiar A-model and B-model as special examples. We discuss the deformation theory of generalized complex structures on GCY manifolds from the viewpoint of the topological sigma-model. This investigation leads to an extension of the famous Tian-Todorov theorem to the realm of generalized geometry.