Mathematical Research Letters
Volume 24 (2017)
A Thom–Smale–Witten theorem on manifolds with boundary
Pages: 119 – 151
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. We extend Bismut–Zhang’s approach relying on the deformed Hodge–de Rham operator to the boundary case.
Paper received on 16 September 2013.