English

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.

Keywords

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

R2 v1 2026-06-22T11:34:01.552Z