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.
arXiv Mathematics e-prints
- Pub Date:
- June 2006
- Mathematics - Differential Geometry;
- Mathematics - Geometric Topology
- Version 2. Substantial revise from the first version including a title change. The previous title was "Constructing isospectral manifolds"