| Resumes des articles |
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ix | |
| Abstracts |
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xiii | |
| Introduction |
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xvii | |
| 1 Rigidite d'actions de groupes sur des espaces metriques |
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xvii | |
| 2 Approche algebrique et approche geometrique de la super-rigidite |
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xviii | |
| 3 Quasi-isometries et invariants des actions de groupes |
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xix | |
| 4 Applications harmoniques pour les espaces singuliers, cohomologie bornee |
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xx | |
| 5 Cas de non rigidite: espaces de modules et compactifications |
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xxi | |
| 6 Le present volume |
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xxii | |
| References |
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xxiv | |
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1 Quelques groupes et geometries |
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Symmetric spaces of the non-compact type: differential geometry |
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1 | (38) |
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1 | (1) |
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2 Riemannian preliminaries |
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2 | (6) |
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3 Riemannian locally symmetric spaces |
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8 | (2) |
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4 Riemannian globally symmetric spaces |
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10 | (7) |
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5 Riemannian manifolds of non-positive curvature |
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17 | (11) |
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6 Symmetric spaces of non-compact type |
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28 | (10) |
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38 | (1) |
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Symmetric spaces of the non-compact type: Lie groups |
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39 | (38) |
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39 | (1) |
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2 Lie groups and Lie algebras: an overview |
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39 | (18) |
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57 | (8) |
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65 | (3) |
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5 Invariant connections on homogeneous spaces |
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68 | (8) |
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76 | (1) |
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77 | (40) |
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1 Groups generated by reflections and apartments |
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78 | (2) |
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2 Linear reflection groups |
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80 | (3) |
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3 General reflection groups |
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83 | (1) |
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4 Discrete reflection groups |
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84 | (2) |
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5 Facets for general reflection groups |
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86 | (2) |
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6 Definitions and general properties |
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88 | (6) |
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7 Metric properties of buildings |
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94 | (1) |
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8 Discrete Euclidean buildings |
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95 | (5) |
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9 Apartments and points at infinity |
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100 | (4) |
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104 | (3) |
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11 Reductive groups over local fields |
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107 | (4) |
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12 The Bruhat-Tits building of GLn |
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111 | (3) |
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114 | (3) |
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Five lectures on lattices in semisimple Lie groups |
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117 | (60) |
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117 | (2) |
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1 Lecture on Coxeter Groups |
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119 | (9) |
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2 Lecture on Arithmetic groups |
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128 | (13) |
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3 Lecture on Representations |
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141 | (12) |
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153 | (13) |
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5 Lecture on Local Fields |
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166 | (8) |
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174 | (3) |
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2 Quelques rigidites en geometrie differentielle |
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Calabi-Weil infinitesimal rigidity |
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177 | (24) |
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177 | (2) |
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1 Deformations and cohomology |
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179 | (1) |
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180 | (1) |
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181 | (2) |
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183 | (3) |
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186 | (3) |
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189 | (3) |
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7 Applications II: Semi-simple groups |
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192 | (7) |
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8 Extensions of this technique |
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199 | (1) |
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199 | (2) |
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Quasi-conformal geometry and Mostow rigidity |
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201 | (12) |
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1 Quasi-conformal geometry |
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201 | (5) |
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206 | (1) |
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3 Mostow rigidity (proof) |
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207 | (1) |
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4 Sullivan-Tukia's theorem (proof) |
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208 | (3) |
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211 | (2) |
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213 | (30) |
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213 | (3) |
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2 Zero or non-zero minimal volume |
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216 | (5) |
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3 Minimal volume and rigidity |
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221 | (2) |
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4 Structure of the proofs of the volume rigidity theorems |
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223 | (2) |
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225 | (13) |
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6 Proof of the minimal volume rigidity theorem: the end |
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238 | (3) |
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241 | (2) |
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A useful formula from bounded cohomology |
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243 | (50) |
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243 | (3) |
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2 Bounded Cohomology Preliminaries |
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246 | (20) |
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3 First Applications of "The Formula" |
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266 | (6) |
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4 Toward "The Formula" with Coefficients |
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272 | (9) |
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5 One More Application of "The Formula": Deformation Rigidity of Lattices of Hyperbolic Isometries |
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281 | (4) |
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A Proof of Proposition 4.1 |
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285 | (3) |
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288 | (5) |
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3 Espaces metriques singuliers |
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Critical exponents and rigidity in negative curvature |
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293 | (28) |
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293 | (5) |
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2 Alternative proof of the theorem 1.5 in a simpler case |
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298 | (5) |
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303 | (1) |
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4 Weak tangent and self similarity of limit sets |
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304 | (5) |
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5 Topological dimension and regular maps |
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309 | (5) |
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6 Topological dimension and Hausdorff dimension |
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314 | (3) |
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7 Proof of the theorem 1.5 |
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317 | (1) |
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318 | (3) |
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Quasi-isometry rigidity of groups |
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321 | (52) |
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1 Preliminaries on quasi-isometries |
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322 | (4) |
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2 Rigidity of non-uniform rank-one lattices |
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326 | (10) |
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3 Classes of groups complete with respect to quasi-isometries |
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336 | (5) |
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4 Asymptotic cones of a metric space |
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341 | (6) |
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5 Relatively hyperbolic groups: image from infinitely far away and rigidity |
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347 | (10) |
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6 Groups asymptotically with(out) cut-points |
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357 | (5) |
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362 | (1) |
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363 | (4) |
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367 | (6) |
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Superrigidite geometrique et applications harmoniques |
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373 | (48) |
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373 | (4) |
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2 Superrigidite et finitude des representations |
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377 | (5) |
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3 Applications harmoniques equivariantes |
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382 | (2) |
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4 Applications harmoniques combinatoires |
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384 | (7) |
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391 | (7) |
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6 Calculs de bas de spectre |
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398 | (16) |
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7 Modeles de groupes aleatoires a densite |
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414 | (2) |
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416 | (5) |
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4 Deformations, espaces de modules et compactifications |
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Sur la compactification de Thurston de l'espace de Teichmuller |
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421 | (24) |
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440 | (5) |
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Moduli of cubic surfaces and Hodge theory (after All-cock, Carlson, Toledo) |
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445 | |
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445 | (1) |
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1 Motivation: the case of quartic surfaces |
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446 | (2) |
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2 Statement of the main result |
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448 | (3) |
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3 The differential of the period map |
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451 | (2) |
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4 Injectivity of the period map |
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453 | (3) |
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456 | (2) |
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6 Stable and semi-stable cubic surfaces |
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458 | (3) |
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7 Extension of the period map |
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461 | (2) |
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463 | (2) |
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465 | |
