nLab
Mostow rigidity theorem

Contents

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:

  • Marc Bourdon, Mostow type rigidity theorems, In: Handbook of Group Actions (Vol. IV), Advanced Lectures in Mathematics 41, Ch. 4, pp. 139–188, International Press 2018 (pdf, book toc pdf)

See also

Last revised on January 2, 2020 at 09:15:46. See the history of this page for a list of all contributions to it.