Contents Online
Mathematical Research Letters
Volume 21 (2014)
Number 1
The genus spectrum of a hyperbolic 3-manifold
Pages: 169 – 185
DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n1.a14
Authors
Abstract
In this paper, 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.
Accepted 30 October 2013
Published 25 July 2014