Determining hyperbolic 3-manifolds by their surfaces

2015/11/01 by McReynolds, D. B., Reid, A. W.
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1511.00222

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.

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