Three-dimensional topological field theory and symplectic algebraic geometry II

Understand

Motivated by the path integral analysis of boundary conditions in a 3-dimensional topological sigma-model, we suggest a definition of the 2-category associated with a holomorphic symplectic manifold X and study its properties.

• The simplest objects of this 2-category are holomorphic lagrangian submanifolds of X.
• We pay special attention to the case when X is the total space of the cotangent bundle of a complex manifold U or a deformation thereof.
• In the latter case the endomorphism category of the zero section is a monoidal category which is an A-infinity deformation of the 2-periodic derived category of U.