Morse homotopy and Chern-Simons perturbation theory

Abstract

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