Determining hyperbolic 3-manifolds by their surfaces

McReynolds, D.; Reid, A.

doi:10.1090/proc/14219

Determining hyperbolic 3-manifolds by their surfaces
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by D. B. McReynolds and A. W. Reid PDF

Proc. Amer. Math. Soc. 147 (2019), 443-450 Request permission

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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