Morse homotopy and Chern-Simons perturbation theory (Q1924114)

The author defines an invariant of a three-dimensional 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. The author conjectures that this invariant coincides with Chern-Simons perturbation theory by Axelrod-Singer et al., and gives a heuristic argument in this direction. There is also a theorem which gives a relation of the construction to open string theory on the cotangent bundle.