Mostow rigidity theorem: Difference between revisions
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{{metric rigidity theorem}} | |||
{{relating Riemannian metric to topology}} | |||
==Statement== | ==Statement== | ||
===Verbal statement=== | ===Verbal statement=== | ||
Any isomorphism between the fundamental groups of two [[hyperbolic manifold]]s of the same dimension and of finite volume, is induced by | Any isomorphism between the fundamental groups of two [[hyperbolic manifold]]s of the same dimension and of finite volume, is induced by a [[Riemannian isometry]]. | ||
==Related results== | ==Related results== | ||
Latest revision as of 19:50, 18 May 2008
Template:Metric rigidity theorem This result relates constructs based on the Riemannian metric to purely topological constructs
Statement
Verbal statement
Any isomorphism between the fundamental groups of two hyperbolic manifolds of the same dimension and of finite volume, is induced by a Riemannian isometry.