The perturbative Chern-Simons theory is studied in a finite-dimensional
version or assuming that the propagator satisfies certain properties (as is the
case, e.g., with the propagator defined by Axelrod and Singer). It turns out
that the effective BV action is a function on cohomology (with shifted degrees)
that solves the quantum master equation and is defined modulo certain canonical
transformations that can be characterized completely. Out of it one obtains
invariants.
We introduce the notion of symplectic microfolds and symplectic
micromorphisms between them. They form a monoidal category, which is a version
of the "category" of symplectic manifolds and canonical relations obtained by
localizing them around lagrangian submanifolds in the spirit of Milnor's
microbundles.