Geometric Structures Laboratory

To any translational invariant generalized complex structure J on a torus T^{2n} we associate a generalized derived category D(J) in terms of deforming the derived category of certain complex structures. This involves the choice of a complex structure, bivector and B-field. Our main result is that the category D(J) is, up to A_\infty quasi-equivalence, independent of the choices involved. We prove that D(J) is also left invariant under the action of T-duality. In particular, the definition is consistent with the homological mirror symmetry conjecture, so that e.g. D(J_\omega) = DFuk(\omega) if mirror symmetry for \omega is known. If time permits, we discuss examples of generalized branes. The talk is based on joint work with Jonathan Block, Vicente Cortés, Julian Holstein, Markus Röser and Aldo Witte.

The talk will be about 50 minutes and the remaining time is meant for questions/discussion.