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Mostow rigidity theorem

In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group and hence unique. The theorem was proven for closed manifolds by Mostow (1968) and extended to…

Applications, The theorem & Overview

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The theorem

Lie groups Hyperbolic space Properly discontinuously Complete Volume form

12 related topics

Applications

Circle packing representations Triangulated planar graphs Geometric group theory Hyperbolic groups Quasi-isometric

6 related topics

Overview

Mathematics Hyperbolic manifold Fundamental group Closed manifolds Mostow

12 related topics

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Overview

Mathematics
Hyperbolic manifold
Fundamental group
Closed manifolds Closed manifold
Mostow George Mostow
Besson, Courtois & Gallot (1996) Mostow rigidity theorem
Prasad Gopal Prasad
Gromov norm
Genus Genus (mathematics)
Moduli space
Diffeomorphism
Teichmüller theory

The theorem

Lie groups Lie group
Hyperbolic space
Properly discontinuously Group action (mathematics)
Complete Riemannian manifold
Volume form
Isomorphism
Homotopy equivalence
Projective orthogonal group
Quadratic form of signature Quadratic form
Lattices Lattice (discrete subgroup)
Locally symmetric spaces Locally symmetric space
Simple Lie groups Simple Lie group

Applications

Circle packing representations Circle packing theorem
Triangulated planar graphs Planar graph
Geometric group theory
Hyperbolic groups Hyperbolic group
Quasi-isometric Quasi-isometry
Commensurable Commensurability (group theory)

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Mostow rigidity theorem

Nodes34

Edges33

Triples11

Avg. degree1.94

Density0.058824

Components1

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Mostow rigidity theorem

Top relations

related to Geometric form · 7

Mostow rigidity theorem → Gamma, Here, If, It, Let, Riemannian, The Mostow

has application · 4

Mostow rigidity theorem → It, Mostow, Out, Thurston

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Important terminology

rigidity hyperbolic mostow displaystyle theorem complete group theory volume finite dimension manifolds proof prasad lattices doi groups mathbb manifold space

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Mostow rigidity theorem	has application	It	0.60	section
Mostow rigidity theorem	has application	Mostow	0.60	section
Mostow rigidity theorem	has application	Out	0.60	section
Mostow rigidity theorem	has application	Thurston	0.60	section
Mostow rigidity theorem	related to Geometric form	Let	0.60	section
Mostow rigidity theorem	related to Geometric form	Riemannian	0.60	section
Mostow rigidity theorem	related to Geometric form	It	0.60	section
Mostow rigidity theorem	related to Geometric form	The Mostow	0.60	section
Mostow rigidity theorem	related to Geometric form	Here	0.60	section
Mostow rigidity theorem	related to Geometric form	If	0.60	section
Mostow rigidity theorem	related to Geometric form	Gamma	0.60	section

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