Index theory of the de Rham complex on manifolds with periodic ends
Geometric Topology
2015-05-27 v1 Analysis of PDEs
Differential Geometry
Abstract
We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \to H_*(X'). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.
Keywords
Cite
@article{arxiv.1310.4246,
title = {Index theory of the de Rham complex on manifolds with periodic ends},
author = {Tomasz Mrowka and Daniel Ruberman and Nikolai Saveliev},
journal= {arXiv preprint arXiv:1310.4246},
year = {2015}
}