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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).

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Book Details

ISBN: 9780521887205
ISBN-10: 0521887208
Format: Hardback
(228mm x 152mm x 29mm)
Pages: 486
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 17-Apr-2008
Country of Publication: United Kingdom

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Author Biography - Bachir Bekka

Bachir Bekka is Professor of Mathematics at the Universite de Rennes 1, France. Pierre de la Harpe is Professor of Mathematics at the Universite de Geneve, Switzerland. Alain Valette is Professor of Mathematics at the Universite de Neuchatel, Switzerland.