Topological strings in generalized complex space

A two-dimensional topological sigma-model on a generalized Calabi-Yau target space X is defined. The model is constructed in a Batalin-Vilkovisky formalism using only a generalized complex structure J and a pure spinor p on X. In the present construction, the algebra of Q-transformations automatically closes off-shell, the model transparently depends only on J, the algebra of observables and correlation functions for topologically trivial maps in genus zero are easily defined. The extended moduli space appears naturally. The familiar action of the twisted N = 2 conformal field theory (CFT) can be recovered after a gauge fixing. In the open case, we consider an example of generalized deformation of complex structure by a holomorphic Poisson bivector beta and recover holomorphic noncommutative Kontsevich *-product.