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'''Mostow rigidity''' is the theorem, proved by George Mostow in 1968, that the geometry of a closed hyperbolic manifold of dimension at least three is completely determined by its fundamental group. Unlike surfaces, where hyperbolic structures vary in Teichmüller space, higher-dimensional hyperbolic manifolds are rigid: any isomorphism of fundamental groups is induced by a unique isometry. This rigidity creates a profound bridge between the algebraic world of group theory and the geometric world of [[Hyperbolic Geometry|hyperbolic geometry]], and it underpins the uniqueness claims in the [[Thurston's geometrization conjecture|geometrization program]] by ensuring that when a 3-manifold is hyperbolic, its geometry is not merely one option among many but the only option.

[[Category:Mathematics]] [[Category:Geometry]]