Constructing Isospectral manifolds.
D. B. McReynolds
This article aims at constructing nonisometric, isospectral manifolds modelled on semisimple Lie groups with finite center and no compact factors. Our two main results are the construction of arbitrarily large sets of closed, isospectral, nonisometric manifolds and pairs of infinite towers of finite covers that are isospectral and nonisometric at each stage. In infinitely many settings, there were no preexisting examples. We also show the growth of these large sets of isospectral manifolds as a function of volume is super-polynomial. Our approach combines ideas from earlier constructions of Spatzier and Brooks--Gornet--Gustafson, and extends the main results of both.