Ergodic Theory and Semisimple Groups (Monographs in Mathematics)

Title......Page 1
ISBN......Page 2
Dedication......Page 3
Table of Contents......Page 5
Preface......Page 7
1.1 Statement of some main results......Page 9
1.2 Outline of the succeeding chapters......Page 13
2.1 Ergodicity and smoothness......Page 16
2.2 Moore\'s Theorem: Statement and Some Consequences......Page 25
2.3 Unitary representations of semi-direct products, I......Page 31
2.4 Vanishing of matrix coefficients for semisimple groups......Page 36
3. 1 Review of algebraic groups......Page 40
3.2 Orbits of measures on projective varieties and the Borel density theorem......Page 46
3.3 Orbits in function spaces......Page 57
3.4 Rationality of measurable mappings - first results......Page 60
3.5 A homomorphism theorem......Page 64
4.1 Amenable groups......Page 67
4.2 Cocycles......Page 73
4.3 Amenable actions......Page 85
5.1 Margulis\' superrigidity theorem and the Mostow-Margulis rigidity theorem......Page 93
5.2 Rigidity and orbit equivalence of ergodic actions......Page 103
6.1 Arithmeticity in groups of R-rank >=r 2 ......Page 122
6.2 The commensurability criterion......Page 130
7.1 Kazhdan\'s property and some consequences......Page 138
7.2 Amenability and unitary representations......Page 141
7.3 Unitary representations and semi-direct products, II......Page 147
7.4 Kazhdan\'s property for semisimple groups......Page 154
8.1 Margulis\' finiteness theorem - statement and first steps of proof......Page 157
8.2 Contracting automorphisms of groups......Page 160
8.3 Completion of the proof - equivariant measurable quotients of flag varieties......Page 165
9.1 Cocycles and Kazhdan\'s property......Page 170
9.2 The algebraic hull of a cocycle......Page 174
9.3 Actions of lattices and product actions......Page 177
9.4 Rigidity and entropy......Page 183
B Dense orbits......Page 191
E Topological quotients of Γ-actions ......Page 193
10 Generalizations to p-adicgroups and S-arithmetic groups......Page 195
A. Borel spaces......Page 202
B. Almost everywhere identities on groups......Page 205
References......Page 210
Subject Index......Page 216