Witten deformations, geometry and dynamics

In this thesis, we study the Morse theory of a function on a manifold from three different point of views: Witten Deformations of the De Rham complex, the homological approach à la Floer, and Harvey-Lawson theory. To tie all of these approaches together, we show through the dynamical approach of Harvey and Lawson that the subcomplex of the complex of differential forms given by eigenforms of the Witten Laplacian is isomorphic to the Morse complex of the Morse function in study.