Kazhdan's property (T) /
Bachir Bekka, Pierre de la Harpe and Alain Valette.
- Cambridge : Cambridge University Press, 2008.
- 1 online resource (xiii, 472 pages) : digital, PDF file(s).
- New mathematical monographs ; 11 .
- New mathematical monographs ; 11. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Definitions, first consequences, and basic examples -- Property (FH) -- Reduced cohomology -- Bounded generation -- A spectral criterion for property (T) -- Some applications of property (T) -- A short list of open questions -- Unitary group representations -- Measures on homogeneous spaces -- Functions of positive type and GNS construction -- Unitary Representations of locally compact abelian groups -- Induced representations -- Weak containment and Fell's topology -- Amenability.
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).