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Kazhdan's Property (T)


Part of New Mathematical Monographs

  • Date Published: April 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521887205


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About the Authors
  • 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).

    • Introduces a very active area of research with applications to topological group theory, measure theory, ergodic theory, random walks, combinatorics, and more
    • The Appendix acts as an introduction to numerous important subjects of mathematics, plus as a first course on representation theory on Hilbert spaces
    • Includes lots of examples and avoids unnecessary technicalities, ensuring it is accessible to students as well as academic researchers
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    Product details

    • Date Published: April 2008
    • format: Hardback
    • isbn: 9780521887205
    • length: 486 pages
    • dimensions: 233 x 161 x 29 mm
    • weight: 0.8kg
    • contains: 6 b/w illus. 4 tables 125 exercises
    • availability: Available
  • Table of Contents

    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
    List of symbols

  • Authors

    Bachir Bekka, Université de Rennes I, France
    Bachir Bekka is Professor of Mathematics at the Université de Rennes 1, France.

    Pierre de la Harpe, Université de Genève
    Pierre de la Harpe is Professor of Mathematics at the Université de Genève, Switzerland.

    Alain Valette, Université de Neuchâtel, Switzerland
    Alain Valette is Professor of Mathematics at the Université de Neuchâtel, Switzerland.

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