The genus spectrum of a hyperbolic 3-manifold
Geometric Topology
2016-11-16 v1
Abstract
In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the commensurability class. In addition, we show that any finite volume hyperbolic 3-manifold has many pairs of non-isometric finite covers with identical spectra. Forgetting multiplicities, we can also construct pairs where the volume ratio is unbounded.
Keywords
Cite
@article{arxiv.0901.4086,
title = {The genus spectrum of a hyperbolic 3-manifold},
author = {D. B. McReynolds and Alan W. Reid},
journal= {arXiv preprint arXiv:0901.4086},
year = {2016}
}