nLab
Mostow rigidity theorem

Context

Riemannian geometry

Manifolds and cobordisms

Contents

Statement

If a 3-manifold Σ\Sigma (or more generally a smooth manifold of dimension 3\geq 3) admits the structure of a hyperbolic manifold of finite volume, then this structure is unique up to isometry, and in fact it is uniquely determined already by the fundamental group π 1(Σ)\pi_1(\Sigma).

(Mostow 68).

References

The original article:

Review:

See also