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 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*(X)→H*(X). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.