Softcover ISBN:  9781470412258 
Product Code:  SURV/67.S 
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Electronic ISBN:  9781470412944 
Product Code:  SURV/67.E 
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Book DetailsMathematical Surveys and MonographsVolume: 67; 2000; 260 ppMSC: 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.
ReadershipGraduate students and research mathematicians working in continuous cohomology.

Table of Contents

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. Noncocompact $S$arithmetic subgroups


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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.

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. Noncocompact $S$arithmetic subgroups