A finiteness theorem for hyperbolic 3-manifolds

Abstract

We prove that there are only finitely many closed hyperbolic 3-manifolds with injectivity radius and first eigenvalue of the Laplacian bounded below whose fundamental groups can be generated by a given number of elements. An application to arithmetic manifolds is also given.

20 pages, to appear in Journal of the London Mathematical Society

References in corpus (3)

• Tameness of hyperbolic 3-manifolds
• The rank of the fundamental group of certain hyperbolic 3-manifolds fibering over the circle
• Geometry and Rank of Fibered Hyperbolic 3-Manifolds

Cited by in corpus (5)

• On the convergence of arithmetic orbifolds
• Uniform models and short curves for random 3-manifolds
• A note on the uniqueness of minimal length carrier graphs
• Harmonic Forms, Minimal Surfaces and Norms on Cohomology of Hyperbolic $3$-Manifolds
• Lengths of edges in carrier graphs