  Quantum Chern-Simons invariants of differentiable manifolds are analyzed from
the point of view of homological algebra. Given a manifold M and a Lie (or,
more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has
the structure of an L-infinity algebra whose homotopy type is a homotopy
invariant of M. We formulate necessary and sufficient conditions for this
L-infinity algebra to have a quantum lift. We also obtain structural results on
unimodular L-infinity algebras and introduce a doubling construction which
links unimodular and cyclic L-infinity algebras.
