Mostow rigidity on the line: A survey

1988 ◽  
pp. 1-12 ◽  
Author(s):  
Stephen Agard
Keyword(s):  
Mostow Rigidity

Smooth cocycle rigidity for expanding maps, and an application to Mostow rigidity

2002 ◽  
Vol 132 (3) ◽  
pp. 439-452 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Lie Group ◽  
Piecewise Smooth ◽  
Rigidity Theorem ◽  
Compact Lie Group ◽  
Expanding Maps ◽  
Cocycle Rigidity ◽  
Mostow Rigidity

We give a variation on the proof of Mostow's rigidity theorem, for certain hyperbolic 3-manifolds. This is based on a rigidity theorem for conjugacies between piecewise-conformal expanding Markov maps. The conjugacy rigidity theorem is deduced from a Livsic cocycle rigidity theorem that we prove for smooth, compact Lie group-valued cocycles over piecewise smooth expanding Markov maps.

scholarly journals On Mostow rigidity for variable negative curvature

Topology ◽  
2002 ◽  
Vol 41 (2) ◽  
pp. 341-361 ◽  
Author(s):  
Igor Belegradek
Keyword(s):  
Negative Curvature ◽  
Mostow Rigidity

scholarly journals GENERALIZED TEICHMULLER SPACE OF NON-COMPACT 3-MANIFOLDS AND MOSTOW RIGIDITY

2010 ◽  
Vol 62 (4) ◽  
pp. 871-889
Author(s):  
C. Charitos ◽  
I. Papadoperakis
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Mostow Rigidity

scholarly journals Quasiregular self-mappings of manifolds and word hyperbolic groups

2007 ◽  
Vol 143 (6) ◽  
pp. 1613-1622 ◽  
Author(s):  
Martin Bridson ◽  
Aimo Hinkkanen ◽  
Gaven Martin
Keyword(s):  
Hyperbolic Group ◽  
Quasiregular Mapping ◽  
Hyperbolic Groups ◽  
Quasiregular Mappings ◽  
Word Hyperbolic Group ◽  
Word Hyperbolic Groups ◽  
Mostow Rigidity ◽  
Negative Sectional Curvature ◽  
Free Word ◽  
Torsion Free

AbstractAn extension of a result of Sela shows that if Γ is a torsion-free word hyperbolic group, then the only homomorphisms Γ→Γ with finite-index image are the automorphisms. It follows from this result and properties of quasiregular mappings, that if M is a closed Riemannian n-manifold with negative sectional curvature ($n\neq 4$), then every quasiregular mapping f:M→M is a homeomorphism. In the constant-curvature case the dimension restriction is not necessary and Mostow rigidity implies that f is homotopic to an isometry. This is to be contrasted with the fact that every such manifold admits a non-homeomorphic light open self-mapping. We present similar results for more general quotients of hyperbolic space and quasiregular mappings between them. For instance, we establish that besides covering projections there are no π1-injective proper quasiregular mappings f:M→N between hyperbolic 3-manifolds M and N with non-elementary fundamental group.

scholarly journals Einstein metrics and Mostow rigidity

1995 ◽  
Vol 2 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Claude LeBrun
Keyword(s):  
Einstein Metrics ◽  
Mostow Rigidity
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