Three-dimensional topological field theory and symplectic algebraic geometry II

Details Three-dimensional topological field theory and symplectic algebraic geometry II Three-dimensional topological field theory and symplectic algebraic geometry II

2009-09-20

arxiv.org/abs/0909.3643v2

Mathematics

Algebraic Geometry

71 pages

Scientific paper

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.

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