Division Algebras and Non-Commensurable Isospectral Manifolds

Alexander Lubotzky, Beth Samuels, Uzi Vishne

A. Reid showed that if ${\Gamma }_1$ and ${\Gamma }_2$ are arithmetic lattices in $G={\mathrm{PGL}}_2(\mathbb{R})$ or in ${\mathrm{PGL}}_2(\mathbb{C})$ which give rise to isospectral manif…