Rigidity in dynamics and geometry: contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 492 S. graph. Darst. |
| ISBN: | 3540432434 |
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MARC
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| 245 | 1 | 0 | |a Rigidity in dynamics and geometry |b contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 |c Marc Burger ... (eds.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XIII, 492 S. |b graph. Darst. | ||
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| 650 | 4 | |a Théorie ergodique - Congrès | |
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| 650 | 4 | |a Geometric group theory |v Congresses | |
| 650 | 4 | |a Rigidity (Geometry) |v Congresses | |
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Record in the Search Index
| _version_ | 1804129131195006976 |
|---|---|
| adam_text | Contents
Quasi Conformal Geometry and Hyperbolic Geometry 1
Marc Bourdon, Herve Pajot
1 Introduction 1
2 Basic Tools in Geometric Function Theory
and Quasi Conformal Geometry 1
3 Gromov Hyperbolic Groups: a Motivation
for Quasi Conformal Geometry 5
4 Further Properties of Loewner Spaces
and Spaces with Poincare Inequalities 8
5 Differentiability of Quasi Symmetric
Homeomorphisms, Applications
to Quasi Isometry 11
References 15
On and Around the Bounded Cohomology of SL2 19
Marc Burger, Nicolas Monod
1 Introduction 19
2 Notations and Conventions 22
3 A Differential Group 23
4 Constructing Cocycles 29
5 Above Degree Two 33
References 36
Densite d orbites d actions de groupes lineaires et proprietes
d equidistribution de marches aleatoires 39
Jean Pierre Conze, Yves Guivarc h
1 Introduction 39
2 Ensemble limite, ensemble asymptotique 41
3 Densite d orbites de T dans Lr(Kd) et equirepartition 47
4 Actions sur les varietes de drapeaux homogenes 59
5 La methode des equations fonctionnelles 62
6 Actions des sous groupes N et A sur T G et F G/M 68
References 74
Exceptional Sets in Dynamical Systems
and Diophantine Approximation 77
Maurice Dodson
1 Introduction 77
2 Rotation Number 78
3 Very Well Approximable Numbers
and Khintchine s Theorem 82
VIII Contents
4 Kolmogorov Arnol d Moser (KAM) Theory 84
5 Linearisation 87
6 Diophantine Approximation in Hyperbolic Geometry 89
7 Extremal Manifolds and Flows 93
8 Conclusion 94
References 95
An Introduction to Cocycle Super Rigidity 99
Renato Feres
1 Introduction 99
2 Cocycles over Group Actions 100
3 Cocycles and Principal Bundle Actions 105
4 Semisimple Lie Groups, in a Hurry 113
5 All the Ergodic Theory We Need 117
6 The Algebraic Hull 120
7 Super Rigidity 123
8 The Proof 124
9 A Few Immediate Applications 131
References 133
Rigid Geometric Structures and Representations
of Fundamental Groups 135
David Fisher
1 Introduction 135
2 Rigid Structures, Killing Fields and Representations
of Fundamental Groups 137
3 Representations of the Fundamental Group
and Dynamics of the Action 139
4 Constructing Quotients from Representations of tt 143
References 146
Coarse Geometric Perspective on Negatively Curved
Manifolds and Groups 149
Alex Furman
1 Introduction 149
2 The Geometric Setup 150
3 Basic Notions of the Coarse Geometric Setup 155
4 Some Results 159
References 165
On Orbit Equivalence of Measure Preserving Actions 167
Damien Gaboriau
1 Equivalence Relations 167
2 Measure Equivalence 170
3 Cost of an Equivalence Relation 174
4 E2 Betti Numbers for Groups 177
Contents IX
5 Simplicial Actions of an Equivalence Relation 180
6 Actions of the Equivalence Relation on a Simplicial Complex 182
7 I2 Betti Numbers for Equivalence Relations and Their Actions 183
References 184
The Margulis Invariant of Isometric Actions
on Minkowski (2+l) Space 187
William M. Goldman
1 Introduction 187
2 Affine Representations 188
3 Lorentzian Geometry 190
4 Deformation Theory 191
5 Properness 194
6 Linear Growth 195
7 Triangle Group Deformations 196
References 198
Diophantine Approximation in Negatively Curved Manifolds
and in the Heisenberg Group 203
Sa ar Hersonsky, Frederic Paulin
1 Introduction 203
2 The Survey Part 204
3 Diophantine Approximation in the Heisenberg Group 213
References 225
Appendix: Diophantine Approximation
on Hyperbolic Surfaces 227
Jouni Parkkonen, Frederic Paulin
References 236
Bounded Cohomology, Boundary Maps, and Rigidity
of Representations into Homeo+(SX) and SU(l,n) 237
Alessandra Iozzi
1 Introduction 237
2 The Euler Class and the Orientation Cocycle 242
3 The Proof of the Formula 243
4 T Equivariant Measurable Maps into JV^S1) 248
5 Semiconjugacy and the Proofs of Matsumoto s
and Goldman s Theorems 251
References 259
SAT Actions and Ergodic Properties
of the Horosphere Foliation 261
Vadim A. Kaimanovich
1 Ergodic Properties of SAT Actions 261
2 The Horosphere Foliation and the Horocycle Flow 265
X Contents
3 Ergodicity of Busemann Cocycles 269
References 280
Nonexpanding Maps, Busemann Functions,
and Multiplicative Ergodic Theory 283
Anders Karlsson
1 Introduction 283
2 Busemann Functions 284
3 Subadditivity 285
4 Nonexpanding Maps with Unbounded Orbit 286
5 Multiplicative Ergodic Theory 288
6 Nonexpansive Iterates in Banach Spaces 291
References 292
The Phase Space of fc Surfaces 295
Frangois Labourie
1 Presentation 295
2 The Geodesic Flow 295
3 One More Dimension 296
4 A Hyperbolic Example 298
5 Geometric Properties of fc Surfaces and Examples 298
6 Phase Space 300
7 Transversal Measure and Coding 302
8 Questions 305
References 307
Schottky Subgroups of Mapping Class Groups
and the Geometry of Surface by Free Groups 309
Lee Mosher
1 Introduction 309
2 Schottky Subgroups of Mapping Class Groups 310
3 Geometry of Surface by Schottky Groups 313
4 Stable Quasi Geodesics in Teichmiiller Space
and the Ending Lamination Conjecture 316
References 318
Actions of Semisimple Lie Groups with Stationary Measure . . 321
Amos Nevo, Robert J. Zimmer
1 Introduction 321
2 Examples of Actions Without an Invariant Measure 322
3 Stationary Measures 323
4 A Structure Theorem for Stationary Measures 326
5 Real Rank One Groups: Some Constructions 328
6 Structure Theorems: Groups of Real Rank at Least Two 330
7 Ergodicity Conditions and the Existence
of Projective Factors of Full Entropy 333
Contents XI
8 Construction of Projective Factors
or Actions of Factor Groups 338
9 Expanding Versus Contracting Automorphisms,
and Margulis Normal Subgroup Theorem 341
References 342
On the Cohomology of Anosov Actions 345
Viorel Nifica, Andrei Torok
1 Cocycles 345
2 Partially Hyperbolic and Anosov Actions 347
3 Livsic Theory 348
4 Regularity Results 351
5 Higher Rank Abelian Actions 353
6 Applications to the Rigidity of Higher Rank Lattice Actions 356
References 359
Harmonic Analysis and Hecke Operators 363
Fee Oh
1 Uniform Pointwise Bounds £s for Matrix Coefficients 363
2 Equidistribution of Hecke Points 367
3 Equidistribution of Integer Points on a Family
of Homogeneous Varieties 370
4 Distributing Points on the Spheres Sn (n 4) 374
References 376
Lp Cohomology and Pinching 379
Pierre Pansu
1 Lp Cohomology 381
2 The Klinneth Formula 383
3 Pinched Manifolds 386
4 Non Vanishing of Torsion 386
5 Vanishing of Torsion for H^ 388
References 388
Classical and Non Linearity Properties
of Kac Moody Lattices 391
Bertrand Remy
1 Introduction 391
2 A Classical Arithmetic Situation and its Geometric Formulation . . . 392
3 Kac Moody Theory and the Generalization 395
4 Questions Arising from the Generalization 400
References 404
XII Contents
Actions of Maximal Tori on Homogeneous Spaces 407
George Tomanov
1 Introduction 407
2 K Algebraic Groups, Arithmetic Subgroups
and Central Simple Algebras 412
3 Reductive Q Subgroups of SLi{A) 416
4 Homogeneous Orbit Closures Containing
Relatively Compact T Orbits 419
5 Closed T Orbits 421
References 423
Dynamics on Parameter Spaces: Submanifold
and Fractal Subset Questions 425
Barak Weiss
1 Introduction 425
2 Conjectures and Results 427
3 A Gentle Reminder Regarding Dynamics
on Homogeneous / Quadratic Differential Spaces 429
4 Quantitative Nondivergence and Applications 432
5 Khinchin s Convergence Case for Fractals 434
6 Logarithm Laws on a Teichmiiller Horocycle 437
References 439
Superrigid Subgroups and Syndetic Hulls
in Solvable Lie Groups 441
Dave Witte
1 What Is a Superrigid Subgroup? 441
2 Other Superrigidity Theorems 445
3 Our Prototypical Proof of Superrigidity 448
4 Solvable Lie Groups and Zariski Closed Subgroups 452
5 Existence of Syndetic Hulls 454
References 457
Square Tiled Surfaces and Teichmuller Volumes
of the Moduli Spaces of Abelian Differentials 459
Anton Zorich
1 Motivations 459
2 Translation Surfaces Versus Flat Surfaces 460
3 Moduli Spaces of Abelian Differentials 461
4 Counting Volume by Means of Counting Integer Points 462
5 Two Examples of Computation 463
A Volumes of Some Strata of Abelian Differentials 467
B Lyapunov Exponents of the Teichmuller Geodesic Flow 467
Contents XIII
C Conjectural Probability P{n) of n Bands
of Trajectories for a Rational Interval
Exchange Transformation 469
References 471
On Property (T) for Discrete Groups 473
Andrzej Zuk
1 Introduction 473
2 Expanders 474
3 How to Prove Property (T) 476
4 Random Groups 478
References 480
Index 483
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| spelling | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 Marc Burger ... (eds.) Berlin [u.a.] Springer 2002 XIII, 492 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Groupes, Théorie géométrique des - Congrès Rigidité (Géométrie) - Congrès Théorie ergodique - Congrès Ergodic theory Congresses Geometric group theory Congresses Rigidity (Geometry) Congresses Starrheit Mathematik (DE-588)4326739-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2000 Cambridge gnd-content Starrheit Mathematik (DE-588)4326739-7 s DE-604 Burger, Marc Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009766051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 Groupes, Théorie géométrique des - Congrès Rigidité (Géométrie) - Congrès Théorie ergodique - Congrès Ergodic theory Congresses Geometric group theory Congresses Rigidity (Geometry) Congresses Starrheit Mathematik (DE-588)4326739-7 gnd |
| subject_GND | (DE-588)4326739-7 (DE-588)1071861417 |
| title | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 |
| title_auth | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 |
| title_exact_search | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 |
| title_full | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 Marc Burger ... (eds.) |
| title_fullStr | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 Marc Burger ... (eds.) |
| title_full_unstemmed | Rigidity in dynamics and geometry contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 Marc Burger ... (eds.) |
| title_short | Rigidity in dynamics and geometry |
| title_sort | rigidity in dynamics and geometry contributions from the programme ergodic theory geometric rigidity and number theory isaac newton institute for the mathematical sciences cambridge united kingdom 5 january 7 july 2000 |
| title_sub | contributions from the programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, United Kingdom, 5 January - 7 July 2000 |
| topic | Groupes, Théorie géométrique des - Congrès Rigidité (Géométrie) - Congrès Théorie ergodique - Congrès Ergodic theory Congresses Geometric group theory Congresses Rigidity (Geometry) Congresses Starrheit Mathematik (DE-588)4326739-7 gnd |
| topic_facet | Groupes, Théorie géométrique des - Congrès Rigidité (Géométrie) - Congrès Théorie ergodique - Congrès Ergodic theory Congresses Geometric group theory Congresses Rigidity (Geometry) Congresses Starrheit Mathematik Konferenzschrift 2000 Cambridge |
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