Isospectral locally symmetric manifolds

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.

Version 2. Substantial revise from the first version including a title change. The previous title was "Constructing isospectral manifolds"

Cited by in corpus (3)

• Non-strongly isospectral spherical space forms
• Arbitrarily large families of spaces of the same volume
• Isospectral towers of Riemannian Manifolds