MORSE HOMOTOPY AND CHERN-SIMONS PERTURBATION-THEORY

We define an invariant of a three manifold equipped with a flat bundle with vanishing homology. The construction is based on Morse theory us ing several Morse functions simultaneously and is regarded as a higher loop analogue of various product operations in algebraic topology. Th ere is a heuristic argument that this invariant is related to perturba tive Chern-Simons Gauge theory by Axelrod-Singer, etc. There is also a theorem which gives a relation of the construction to open string the ory on the cotangent bundle.