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  • Book
  • © 1999

Supersymmetry and Equivariant de Rham Theory

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  • The subject of the book is the equivariant cohomology theory of differentiable manifolds.

  • Although this subject has gained great popularity since the early 1980's, it has not before been the subject of a monograph and so the excellent and long-awaited book fills an important gap It covers almost all important aspects of the subject The authors are key authorities in this field

  • Includes supplementary material: sn.pub/extras

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  • ISBN: 978-3-662-03992-2
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  • Tax calculation will be finalised during checkout
Softcover Book
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxiii
  2. Equivariant Cohomology in Topology

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 1-7
  3. G* Modules

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 9-32
  4. The Weil Algebra

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 33-40
  5. The Weil Model and the Cartan Model

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 41-52
  6. Cartan’s Formula

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 53-59
  7. Spectral Sequences

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 61-76
  8. Fermionic Integration

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 77-93
  9. Characteristic Classes

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 95-110
  10. Equivariant Symplectic Forms

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 111-147
  11. The Thom Class and Localization

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 149-172
  12. The Abstract Localization Theorem

    • Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 173-188
  13. Back Matter

    Pages 189-229

About this book

Equivariant cohomology in the framework of smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Brüning and V. M. Guillemin. The point of departure are two relatively short but very remarkable papers by Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie". These papers are reproduced here, together with a scholarly introduction to the subject from a modern point of view, written by two of the leading experts in the field. This "introduction", however, turns out to be a textbook of its own presenting the first full treatment of equivariant cohomology from the de Rahm theoretic perspective. The well established 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 (like symplectic geometry, Lie theory, dynamical systems, and mathematical physics), leading up to the localization theorems and recent results on the ring structure of the equivariant cohomology.

Keywords

  • Characteristic class
  • Equivariant cohomology theory of differential manifolds
  • cohomology
  • cohomology theory
  • de Rham Theory
  • differential geometry
  • homology theory mathematical physics
  • symplectic geometry

Reviews

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."

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Victor W. Guillemin

  • Department of Mathematics, Harvard University, Cambridge, USA

    Shlomo Sternberg

  • Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät II, Humboldt-Universität Berlin, Berlin, Germany

    Jochen Brüning

About the authors

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."

Bibliographic Information

  • Book Title: Supersymmetry and Equivariant de Rham Theory

  • Authors: Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning

  • DOI: https://doi.org/10.1007/978-3-662-03992-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Hardcover ISBN: 978-3-540-64797-3

  • Softcover ISBN: 978-3-642-08433-1

  • eBook ISBN: 978-3-662-03992-2

  • Edition Number: 1

  • Number of Pages: XXIII, 232

  • Topics: Algebraic Topology, Differential Geometry, Theoretical, Mathematical and Computational Physics

Buying options

eBook
USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-3-662-03992-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 99.99
Price excludes VAT (USA)
Hardcover Book
USD 139.99
Price excludes VAT (USA)