Index theory of the de Rham complex on manifolds with periodic ends

Abstract

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover [tilde over X]→X. The completion of this complex in exponentially weighted L² norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H[subscript ∗] ([tilde over X])→H[subscript ∗] ([tilde over X]). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.