Isospectral locally symmetric manifolds
Differential Geometry
2016-11-16 v2 Geometric Topology
Abstract
In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-polynomial. Finally, we construct pairs of infinite towers of finite covers of a closed manifold that are isospectral and non-isometric at each stage.
Cite
@article{arxiv.math/0606540,
title = {Isospectral locally symmetric manifolds},
author = {D. B. McReynolds},
journal= {arXiv preprint arXiv:math/0606540},
year = {2016}
}
Comments
Version 2. Substantial revise from the first version including a title change. The previous title was "Constructing isospectral manifolds"