Kazhdan's Property (T)

The first comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics.

Bachir Bekka (Author), Pierre de la Harpe (Author), Alain Valette (Author)

9780521887205, Cambridge University Press

Hardback, published 17 April 2008

486 pages, 6 b/w illus. 4 tables 125 exercises
23.3 x 16.1 x 2.9 cm, 0.8 kg

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).

Introduction
Part I. Kazhdan's Property (T): 1. Property (T)
2. Property (FH)
3. Reduced Cohomology
4. Bounded generation
5. A spectral criterion for Property (T)
6. Some applications of Property (T)
7. A short list of open questions
Part II. Background on Unitary Representations: A. Unitary group representations
B. Measures on homogeneous spaces
C. Functions of positive type
D. Representations of abelian groups
E. Induced representations
F. Weak containment and Fell topology
G. Amenability
Appendix
Bibliography
List of symbols
Index.

Subject Areas: Topology [PBP], Groups & group theory [PBG], Algebra [PBF]