  Wedge product on deRham complex of a Riemannian manifold $M$ can be pulled
back to $H^*(M)$ via explicit homotopy, constructed using Green's operator, to
give higher product structures. We prove Fukaya's conjecture which suggests
that Witten deformation of these higher product structures have semiclassical
limits as operators defined by counting gradient flow trees with respect to
Morse functions, which generalizes the remarkable Witten deformation of deRham
differential from a statement concerning homology to one concerning real
homotopy type of $M$. Various applications of this conjecture to mirror
symmetry are also suggested by Fukaya.
