Chapters in this book

1. Frontmatter i
2. Contents v
3. Foreword ix
4. INTRODUCTION 1
5. 1. Spectra and Structure of Ergodic Actions
6. A. Extensions of Ergodic Group Actions 17
7. B. Ergodic Actions with Generalized Discrete Spectrum 54
8. C. Orbit Spaces of Unitary Representations, Ergodic Theory, and Simple Lie Groups 88
9. 2 Amenable Actions, Equivalence Relations, and Foliations
10. A. Amenable Ergodic Group Actions and an Application to Poisson Boundaries of Random Walks 107
11. B. Induced and Amenable Ergodic Actions of Lie Groups 130
12. C. Hyperfinite Factors and Amenable Ergodic Actions, Inventiones mathematicae (1977) 152
13. D. Curvature of Leaves in Amenable Foliations, American journal of Mathematics (1983) 161
14. E. Amenable Actions and Dense Subgroups of Lie Groups Journal of Functional Analysis (1987) 173
15. 3 Orbit Equivalence and Strong Rigidity
16. A. Strong Rigidity for Ergodic Actions of Semisimple Lie Groups, Annals of Mathematics (1980) 183
17. B. Orbit Equivalence and Rigidity of Ergodic Actions of Lie Groups 202
18. C. Ergodic Actions of Semisimple Groups and Product Relations 219
19. 4 Cocycle Superrigidity and the Program to Describe Lie Group and Lattice Actions on Manifolds
20. A. Volume Preserving Actions of Lattices in Semisimple Groups on Compact Manifolds, Institut des Hautes Etudes Scientifiques Publications Mathematiques (1984) 233
21. B. Kazhdan Groups Acting on Compact Manifolds, Inventiones mathematicae (1984) 262
22. C. Actions of Lattices in Semisimple Groups Preserving a G-Structure of Finite Type, Ergodic Theory and Dynamical Systems (1985) 274
23. D. Actions of Semisimple Groups and Discrete Subgroups, Proceedings of the International Congress of Mathematicians, August 3-11, 1986 (1987) 280
24. E. Split Rank and Semisimple Automorphism Groups of G-Structures, journal of Differential Geometry (1987) 292
25. F. Manifolds with Infinitely Many Actions of an Arithmetic Group 297
26. G. Spectrum, Entropy, and Geometric Structures for Smooth Actions of Kazhdan Groups 301
27. H. Cocycle Superrigidity and Rigidity for Lattice Actions on Tori (with Anatole Katok and James Lewis) 317
28. I. Volume-Preserving Actions of Simple Algebraic Q-Groups on Low-Dimensional Manifolds (with Dave Witte Morris) 330
29. 5 Stabilizers of Semisimple Lie Group Actions: Invariant Random Subgroups
30. A. Stabilizers for Ergodic Actions of Higher Rank Semisimple Groups (with Garrett Stuck) 339
31. 6 Representations and Arithmetic Properties of Actions, Fundamental Groups, and Foliations
32. A. Arithmeticity ofHolonomy Groups of Lie Foliations 367
33. B. Representations of Fundamental Groups of Manifolds with a Semisimple Transformation Group 391
34. C. Superrigidity, Ratner's Theorem, and Fundamental Groups 404
35. D. Fundamental Groups of Negatively Curved Manifolds and Actions of Semi simple Groups 413
36. A canonical arithmetic quotient for simple Lie group actions 424
37. F. A Canonical Arithmetic Quotient for Simple Lie Group Actions 437
38. G. Entropy and Arithmetic Quotients for Simple Automorphism Groups of Geometric Manifolds 456
39. H. Geometric Lattice Actions, Entropy and Fundamental Groups 466
40. 7 Geometric Structures: Automorphisms of Geometric Manifolds and Rigid Structures; Locally Homogeneous Manifolds
41. A. On the Automorphism Group of a Compact Lorentz Manifold and Other Geometric Manifolds 481
42. B. Semisimple Automorphism Groups of G-Structures 495
43. C. Automorphism Groups and Fundamental Groups of Geometric Manifolds 502
44. D. Discrete Groups and Non-Riemannian Homogeneous Spaces 520
45. E. On Manifolds Locally Modelled on Non-Riemannian Homogeneous Spaces 530
46. F. On the Non-existence of Cocompact Lattices for SL(n)!SL(m) 541
47. 8 Stationary Measures and Structure Theorems for Lie Group Actions
48. A. A Structure Theorem for Actions of Semisimple Lie Groups 547
49. B. Entropy of Stationary Measures and Bounded Tangential de-Rham Cohomology of Semisimple Lie Group Actions 577
50. C. Invariant Rigid Geometric Structures and Smooth Projective Factors 596
51. GROUPS ACTING ON MANIFOLDS: Around the Zimmer Program 609
52. AFTERWORD: Recent Progress in the Zimmer Program 685
53. Acknowledgments 709