Isospectral locally symmetric manifolds

Details Isospectral locally symmetric manifolds Isospectral locally symmetric manifolds

2006-06-21

arxiv.org/abs/math/0606540v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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