Hardcover ISBN:  9780821826300 
Product Code:  CRMM/15 
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eBook ISBN:  9781470438609 
Product Code:  CRMM/15.E 
List Price:  $110.00 
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AMS Member Price:  $88.00 
Hardcover ISBN:  9780821826300 
eBook: ISBN:  9781470438609 
Product Code:  CRMM/15.B 
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Hardcover ISBN:  9780821826300 
Product Code:  CRMM/15 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
eBook ISBN:  9781470438609 
Product Code:  CRMM/15.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Hardcover ISBN:  9780821826300 
eBook ISBN:  9781470438609 
Product Code:  CRMM/15.B 
List Price:  $225.00 $170.00 
MAA Member Price:  $202.50 $153.00 
AMS Member Price:  $180.00 $136.00 

Book DetailsCRM Monograph SeriesVolume: 15; 2002; 104 ppMSC: Primary 19; Secondary 14
This book contains a complete proof of the fact that Borel's regulator map is twice Beilinson's regulator map. The strategy of the proof follows the argument sketched in Beilinson's original paper and relies on very similar descriptions of the ChernWeil morphisms and the van Est isomorphism.
The book has two different parts. The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. Topics such as simplicial objects, Hopf algebras, characteristic classes, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, continuous group cohomology and the van Est Theorem are discussed.
The second part contains the comparison theorem and the specific material needed in its proof, such as explicit descriptions of the ChernWeil morphism and the van Est isomorphisms, a discussion about small cosimplicial algebras, and a comparison of different definitions of Borel's regulator.
Titles in this series are copublished with the Centre de recherches mathématiques.
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

Introduction

Simplicial and cosimplicial objects

$H$spaces and Hopf algebras

The cohomology of the general linear group

Lie algebra cohomology and the Weil algebra

Group cohomology and the van Est isomorphism

Small cosimplicial algebras

Higher diagonals and differential forms

Borel’s regulator

Beilinson’s regulator


Reviews

Contains a lot of expository material, ... The monograph is extremely valuable, not only in settling the question but in doing so in a readable way.
Mathematical Reviews 
... an excellent background source for graduate students.
Zentralblatt MATH


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This book contains a complete proof of the fact that Borel's regulator map is twice Beilinson's regulator map. The strategy of the proof follows the argument sketched in Beilinson's original paper and relies on very similar descriptions of the ChernWeil morphisms and the van Est isomorphism.
The book has two different parts. The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. Topics such as simplicial objects, Hopf algebras, characteristic classes, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, continuous group cohomology and the van Est Theorem are discussed.
The second part contains the comparison theorem and the specific material needed in its proof, such as explicit descriptions of the ChernWeil morphism and the van Est isomorphisms, a discussion about small cosimplicial algebras, and a comparison of different definitions of Borel's regulator.
Titles in this series are copublished with the Centre de recherches mathématiques.
Graduate students and research mathematicians interested in number theory.

Chapters

Introduction

Simplicial and cosimplicial objects

$H$spaces and Hopf algebras

The cohomology of the general linear group

Lie algebra cohomology and the Weil algebra

Group cohomology and the van Est isomorphism

Small cosimplicial algebras

Higher diagonals and differential forms

Borel’s regulator

Beilinson’s regulator

Contains a lot of expository material, ... The monograph is extremely valuable, not only in settling the question but in doing so in a readable way.
Mathematical Reviews 
... an excellent background source for graduate students.
Zentralblatt MATH