Isospectral towers of Riemannian Manifolds

TL;DR

This paper constructs large families of infinite towers of compact Riemannian manifolds that are isospectral but not isometric, including hyperbolic surfaces and 3-manifolds, beyond Sunada's method.

Contribution

It introduces new methods to build isospectral towers of manifolds in dimensions two and three, not derived from Sunada's technique.

Findings

Constructed arbitrarily large isospectral towers

Demonstrated towers in hyperbolic 2- and 3-manifolds

Showed towers are not from Sunada's method

Abstract

In this paper we construct, for n >= 2, arbitrarily large families of infinite towers of compact, orientable Riemannian n-manifolds which are isospectral but not isometric at each stage. In dimensions two and three, the towers produced consist of hyperbolic 2-manifolds and hyperbolic 3-manifolds, and in these cases we show that the isospectral towers do not arise from Sunada's method.