Kazhdan's Property (T)

by Bachir Bekka , Pierre de la Harpe , Alain Valette

• ISBN13: 9780521887205
• ISBN10: 0521887208
• Format: Hardcover
• Copyright: 2008-06-02
• Publisher: Cambridge University Press

Summary

Property (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).

Table of Contents

Introduction

KazhdanÆs Property (T)

Property (T)

Property (FH)

Reduced Cohomology

Bounded generation

A spectral criterion for Property (T)

Some applications of Property (T)

A short list of open questions

Background on Unitary Representations

Unitary group representations

Measures on homogeneous spaces

Functions of positive type

Representations of abelian groups

Induced representations

Weak containment and Fell topology

Amenability

Appendix

Bibliography

List of symbols

Index

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