On the geometric and topological rigidity of hyperbolic 3-manifolds

Gabai, David

doi:10.1090/S0273-0979-1994-00523-3

On the geometric and topological rigidity of hyperbolic 3-manifolds
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Bull. Amer. Math. Soc. 31 (1994), 228-232 Request permission

Abstract:

A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.

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SnapPea

A computer program for creating and studying hyperbolic

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