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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups: Second Edition

A. Borel Institute for Advanced Study, Princeton, NJ
N. Wallach University of California, San Diego, La Jolla, CA
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Softcover ISBN: 978-1-4704-1225-8
Product Code: SURV/67.S
List Price: $77.00 MAA Member Price:$69.30
AMS Member Price: $61.60 Electronic ISBN: 978-1-4704-1294-4 Product Code: SURV/67.E List Price:$72.00
MAA Member Price: $64.80 AMS Member Price:$57.60
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List Price: $115.50 MAA Member Price:$103.95
AMS Member Price: $92.40 Click above image for expanded view Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups: Second Edition A. Borel Institute for Advanced Study, Princeton, NJ N. Wallach University of California, San Diego, La Jolla, CA Available Formats:  Softcover ISBN: 978-1-4704-1225-8 Product Code: SURV/67.S  List Price:$77.00 MAA Member Price: $69.30 AMS Member Price:$61.60
 Electronic ISBN: 978-1-4704-1294-4 Product Code: SURV/67.E
 List Price: $72.00 MAA Member Price:$64.80 AMS Member Price: $57.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$115.50 MAA Member Price: $103.95 AMS Member Price:$92.40
• Book Details

Mathematical Surveys and Monographs
Volume: 672000; 260 pp
MSC: Primary 22; Secondary 57;

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.

• Chapters
• 0. Notation and preliminaries
• I. Relative Lie algebra cohomology
• II. Scalar product, Laplacian and Casimir element
• III. Cohomology with respect to an induced representation
• IV. The Langlands classification and uniformly bounded representations
• V. Cohomology with coefficients in $\Pi _\infty (G)$
• VI. The computation of certain cohomology groups
• VII. Cohomology of discrete subgroups and Lie algebra cohomology
• VIII. The construction of certain unitary representations and the computation of the corresponding cohomology groups
• IX. Continuous cohomology and differentiable cohomology
• X. Continuous and differentiable cohomology for locally compact totally disconnected groups
• XI. Cohomology with coefficients in $\Pi _\infty (G)$: The $p$-adic case
• XII. Differentiable cohomology for products of real Lie groups and T.D. groups
• XIII. Cohomology of discrete cocompact subgroups
• XIV. Non-cocompact $S$-arithmetic subgroups

• Requests

Review Copy – for reviewers who would like to review an AMS book
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Accessibility – to request an alternate format of an AMS title
Volume: 672000; 260 pp
MSC: Primary 22; Secondary 57;

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.

• Chapters
• 0. Notation and preliminaries
• I. Relative Lie algebra cohomology
• II. Scalar product, Laplacian and Casimir element
• III. Cohomology with respect to an induced representation
• IV. The Langlands classification and uniformly bounded representations
• V. Cohomology with coefficients in $\Pi _\infty (G)$
• VI. The computation of certain cohomology groups
• VII. Cohomology of discrete subgroups and Lie algebra cohomology
• VIII. The construction of certain unitary representations and the computation of the corresponding cohomology groups
• IX. Continuous cohomology and differentiable cohomology
• X. Continuous and differentiable cohomology for locally compact totally disconnected groups
• XI. Cohomology with coefficients in $\Pi _\infty (G)$: The $p$-adic case
• XII. Differentiable cohomology for products of real Lie groups and T.D. groups
• XIII. Cohomology of discrete cocompact subgroups
• XIV. Non-cocompact $S$-arithmetic subgroups
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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