Overview

"Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Bruning and V.W. Guillemin. The point of departure are two relatively short but very remarkable papers be Henry Cartan, published in 1950 in the Proceedings of the ""Colloque de Topologie"". These papers are reproduced here, together with a modern introduction to the subject, written by two of the leading experts in the field. This ""introduction"" comes as a textbook of its own, though, presenting the first full treatment of equivariant cohomology in the de Rahm setting. The well known topological approach is linked with the differential form aspect through the equivariant de Rahm theorem. The systematic use of supersymmetry simplifies considerably the ensuing development of the basic technical tools which are then applied to a variety of subjects, leading up to the localization theorems and other very recent results."

Full Product Details

Author:   Victor W Guillemin ,  Jochen Brüning ,  Shlomo Sternberg
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1999 ed.
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.190kg
ISBN:  

9783540647973

ISBN 10:   354064797
Pages:   232
Publication Date:   04 May 1999
Audience:   College/higher education ,  General/trade ,  Postgraduate, Research & Scholarly ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

1 Equivariant Cohomology in Topology.- 3 The Weil Algebra.- 4 The Weil Model and the Cartan Model.- 5 Cartan’s Formula.- 6 Spectral Sequences.- 7 Fermionic Integration.- 8 Characteristic Classes.- 9 Equivariant Symplectic Forms.- 10 The Thom Class and Localization.- 11 The Abstract Localization Theorem.- Notions d’algèbre différentielle; application aux groupes de Lie et aux variétés où opère un groupe de Lie: Henri Cartan.- La transgression dans un groupe de Lie et dans un espace fibré principal: Henri Cartan.

Reviews

From the reviews: <p>MATHEMATICAL REVIEWS <p> The authors are very generous to the reader, and explain all the basics in a very clear and efficient manner. The understanding is enhanced by appealing to concepts which developed after Cartana (TM)s seminal work, which also help to place things in a broader context. This approach sheds light on many of Cartana (TM)s motivations, and helps the reader appreciate the beauty and the simplicity of his ideasa ]There are a ~giftsa (TM) for the more advanced readers as well, in the form of many refreshing modern points of view proposed by the authorsa ]The second part of the book is in my view a very convincing argument for the usefulness and versatility of this theory, and can also serve as a very good invitation to more detailed investigation. I learned a lot from this book, which is rich in new ideas. I liked the style and the respect the authors have for the readers. I also appreciated very much the bibliographical and historical comments at the end of each chapter. To conclude, I believe this book is a must have for any mathematician/physicist remotely interested in this subject.

From the reviews: MATHEMATICAL REVIEWS The authors are very generous to the reader, and explain all the basics in a very clear and efficient manner. The understanding is enhanced by appealing to concepts which developed after Cartan's seminal work, which also help to place things in a broader context. This approach sheds light on many of Cartan's motivations, and helps the reader appreciate the beauty and the simplicity of his ideas...There are 'gifts' for the more advanced readers as well, in the form of many refreshing modern points of view proposed by the authors...The second part of the book is in my view a very convincing argument for the usefulness and versatility of this theory, and can also serve as a very good invitation to more detailed investigation. I learned a lot from this book, which is rich in new ideas. I liked the style and the respect the authors have for the readers. I also appreciated very much the bibliographical and historical comments at the end of each chapter. To conclude, I believe this book is a must have for any mathematician/physicist remotely interested in this subject.

From the reviews: MATHEMATICAL REVIEWS The authors are very generous to the reader, and explain all the basics in a very clear and efficient manner. The understanding is enhanced by appealing to concepts which developed after Cartan's seminal work, which also help to place things in a broader context. This approach sheds light on many of Cartan's motivations, and helps the reader appreciate the beauty and the simplicity of his ideas...There are `gifts' for the more advanced readers as well, in the form of many refreshing modern points of view proposed by the authors...The second part of the book is in my view a very convincing argument for the usefulness and versatility of this theory, and can also serve as a very good invitation to more detailed investigation. I learned a lot from this book, which is rich in new ideas. I liked the style and the respect the authors have for the readers. I also appreciated very much the bibliographical and historical comments at the end of each chapter. To conclude, I believe this book is a must have for any mathematician/physicist remotely interested in this subject.

Author Information

"From the reviews: MATHEMATICAL REVIEWS ""The authors are very generous to the reader, and explain all the basics in a very clear and efficient manner. The understanding is enhanced by appealing to concepts which developed after Cartan's seminal work, which also help to place things in a broader context. This approach sheds light on many of Cartan's motivations, and helps the reader appreciate the beauty and the simplicity of his ideas...There are 'gifts' for the more advanced readers as well, in the form of many refreshing modern points of view proposed by the authors...The second part of the book is in my view a very convincing argument for the usefulness and versatility of this theory, and can also serve as a very good invitation to more detailed investigation. I learned a lot from this book, which is rich in new ideas. I liked the style and the respect the authors have for the readers. I also appreciated very much the bibliographical and historical comments at the end of each chapter. To conclude, I believe this book is a must have for any mathematician/physicist remotely interested in this subject."""

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions