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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups: Second Edition
A. Borel, Institute for Advanced Study, Princeton, NJ, and N. Wallach, University of California, San Diego, La Jolla, CA

Mathematical Surveys and Monographs
2000; 260 pp; hardcover
Volume: 67
ISBN-10: 0-8218-0851-6
ISBN-13: 978-0-8218-0851-1
List Price: US$68
Member Price: US$54.40
Order Code: SURV/67
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It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.


Graduate students and research mathematicians working in continuous cohomology.

Table of Contents

  • Notation and preliminaries
  • Relative Lie algebra cohomology
  • Scalar product, Laplacian and Casimir element
  • Cohomology with respect to an induced representation
  • The Langlands classification and uniformly bounded representations
  • Cohomology with coefficients in \(\Pi_\infty(G)\)
  • The computation of certain cohomology groups
  • Cohomology of discrete subgroups and Lie algebra cohomology
  • The construction of certain unitary representations and the computation of the corresponding cohomology groups
  • Continuous cohomology and differentiable cohomology
  • Continuous and differentiable cohomology for locally compact totally disconnected groups
  • Cohomology with coefficients in \(\Pi_\infty(G)\): The \(p\)-adic case
  • Differentiable cohomology for products of real Lie groups and t.d. groups
  • Cohomology of discrete cocompact subgroups
  • Noncompact \(S\)-arithmetic subgroups
  • Bibliography
  • Index
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