nLab
hyperbolic 3-manifold

Contents

Context

Riemannian geometry

Manifolds and cobordisms

Contents

Idea

A Riemannian manifold which is both a 3-manifold and a hyperbolic manifold is a hyperbolic 3-manifold.

Equivalently this is a Riemannian manifold which is isometric to the quotient space 3/Γ\mathbb{H}^3/ \Gamma of hyperbolic 3-space by the action of a torsion-free discrete group Γ\Gamma acting by isometries.

Properties

Volume conjecture

For the moment see at volume conjecture.

Examples

References

General

See also

M5-branes wrapped on hyperbolic 3-manifolds

Discussion of black M5-branes wrapped on hyperbolic 3-manifolds:

Suggestion that the statement of the volume conjecture is reall8 AdS-CFT duality combined with the 3d-3d correspondence for M5-branes wrapped on hyperbolic 3-manifolds:

Last revised on September 30, 2019 at 03:54:36. See the history of this page for a list of all contributions to it.