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200 10$aStrong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 /$fG. Daniel Mostow
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1974
215   $a1 online resource (205 pages)
225 0 $aAnnals of Mathematics Studies ;$v247
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08136-0 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tContents -- $t§1. Introduction -- $t§2. Algebraic Preliminaries -- $t§3. The Geometry of ? : Preliminaries -- $t§4. A Metric Definition of the Maximal Boundary -- $t§5. Polar Parts -- $t§6. A Basic Inequality -- $t§7. Geometry of Neighboring Flats -- $t§8. Density Properties of Discrete Subgroups -- $t§8. Density Properties of Discrete Subgroups -- $t§ 10. Pseudo Isometries of Simply Connected Spaces with Negative Curvature -- $t§11. Polar Regular Elements in Co-Compact ? -- $t§ 12. Pseudo-Isometric Invariance of Semi-Simple and Unipotent Elements -- $t§13. The Basic Approximation -- $t§14. The Map ?? -- $t§15. The Boundary Map ?0 -- $t§16. Tits Geometries -- $t§17. Rigidity for R-rank > 1 -- $t§18. The Restriction to Simple Groups -- $t§19. Spaces of R-rank 1 -- $t§20. The Boundary Semi-Metric -- $t§21. Quasi-Conformal Mappings Over K and Absolute Continuity on Almost All R-Circles -- $t§22. The Effect of Ergodicity -- $t§23. R-Rank 1 Rigidity Proof Concluded -- $t§24. Concluding Remarks -- $tBibliography -- $tBackmatter
330   $aLocally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan.The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
410  0$aAnnals of mathematics studies ;$vNumber 78.
606   $aRiemannian manifolds
606   $aSymmetric spaces
606   $aLie groups
606   $aRigidity (Geometry)
610   $aAddition.
610   $aAdjoint representation.
610   $aAffine space.
610   $aApproximation.
610   $aAutomorphism.
610   $aAxiom.
610   $aBig O notation.
610   $aBoundary value problem.
610   $aCohomology.
610   $aCompact Riemann surface.
610   $aCompact space.
610   $aConjecture.
610   $aConstant curvature.
610   $aCorollary.
610   $aCounterexample.
610   $aCovering group.
610   $aCovering space.
610   $aCurvature.
610   $aDiameter.
610   $aDiffeomorphism.
610   $aDifferentiable function.
610   $aDimension.
610   $aDirect product.
610   $aDivision algebra.
610   $aErgodicity.
610   $aErlangen program.
610   $aExistence theorem.
610   $aExponential function.
610   $aFinitely generated group.
610   $aFundamental domain.
610   $aFundamental group.
610   $aGeometry.
610   $aHalf-space (geometry).
610   $aHausdorff distance.
610   $aHermitian matrix.
610   $aHomeomorphism.
610   $aHomomorphism.
610   $aHyperplane.
610   $aIdentity matrix.
610   $aInner automorphism.
610   $aIsometry group.
610   $aJordan algebra.
610   $aMatrix multiplication.
610   $aMetric space.
610   $aMorphism.
610   $aMöbius transformation.
610   $aNormal subgroup.
610   $aNormalizing constant.
610   $aPartially ordered set.
610   $aPermutation.
610   $aProjective space.
610   $aRiemann surface.
610   $aRiemannian geometry.
610   $aSectional curvature.
610   $aSelf-adjoint.
610   $aSet function.
610   $aSmoothness.
610   $aStereographic projection.
610   $aSubgroup.
610   $aSubset.
610   $aSummation.
610   $aSymmetric space.
610   $aTangent space.
610   $aTangent vector.
610   $aTheorem.
610   $aTopology.
610   $aTubular neighborhood.
610   $aTwo-dimensional space.
610   $aUnit sphere.
610   $aVector group.
610   $aWeyl group.
615  0$aRiemannian manifolds.
615  0$aSymmetric spaces.
615  0$aLie groups.
615  0$aRigidity (Geometry)
676   $a516/.36
700   $aMostow$b G. Daniel, $0606388
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154743303321
996   $aStrong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78$92785740
997   $aUNINA