Determining hyperbolic 3-manifolds by their surfaces
Geometric Topology
2018-05-16 v2 Differential Geometry
Group Theory
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.
Cite
@article{arxiv.1511.00222,
title = {Determining hyperbolic 3-manifolds by their surfaces},
author = {D. B. McReynolds and A. W. Reid},
journal= {arXiv preprint arXiv:1511.00222},
year = {2018}
}
Comments
v2. 9 pages. To appear in Proc. Amer. Math. Soc