Determining hyperbolic 3-manifolds by their surfaces

Abstract

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed, orientable, hyperbolic 3-manifolds that have the same set of surfaces.

v2. 9 pages. To appear in Proc. Amer. Math. Soc

References in corpus (4)

• Tameness of hyperbolic 3-manifolds
• Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces
• Geometric spectra and commensurability
• Totally Geodesic Spectra of Quaternionic Hyperbolic Orbifolds