A-infinity Structures from Witten Deformation.

摘要

Given a Morse function on a compact oriented Riemannian manifold, inspired by considerations in Physics, Witten suggested to construct a twisted deRham complex so that each critical point corresponds to an eigenform of Witten Laplacian with small eigenvalue. The method gives another way to study the topology on a manifold, which is known as Witten deformation. This thesis further apply Witten's idea and homological perturbation lemma to construct a deRham category with an A1 structures and shows the correspondence between this deRham category and the Morse category.