  Given a smooth compact manifold with boundary, we show that the subcomplex of
the deformed de Rham complex consisting of eigenspaces of small eigenvalues of
the Witten Laplacian is canonically isomorphic to the Thom-Smale complex
constructed by Laudenbach. Our proof is based on Bismut-Lebeau's analytic
localization techniques. As a by-product, we obtain Morse inequalities for
manifolds with boundary.
