Isospectral locally symmetric manifolds

TL;DR

This paper constructs large sets of isospectral, non-isometric locally symmetric manifolds, demonstrating their growth and providing infinite towers of such manifolds, advancing understanding of spectral geometry.

Contribution

It introduces methods to construct arbitrarily large sets of isospectral, non-isometric manifolds and analyzes their growth relative to volume, including infinite towers.

Findings

Constructed arbitrarily large sets of isospectral, non-isometric manifolds

Showed super-polynomial growth of these sets with volume

Built infinite towers of isospectral, non-isometric finite covers

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.