Using the Alexandrov–Kontsevich–Schwarz–Zaboronsky (AKSZ) prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of as 2D and 3D generalizations of A- and B-models. Within the BV framework we show that the 3D model on a two-manifold cross an interval can be reduced to the 2D model.
"2D and 3D topological field theories for generalized complex geometry." Adv. Theor. Math. Phys. 14 (2) 695 - 725, April 20.