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Supersymmetry and Equivariant de Rham Theory

  • Victor W. Guillemin
  • Shlomo Sternberg
  • Jochen Brüning

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 1-7
  3. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 9-32
  4. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 33-40
  5. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 41-52
  6. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 53-59
  7. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 61-76
  8. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 77-93
  9. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 95-110
  10. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 111-147
  11. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 149-172
  12. Victor W. Guillemin, Shlomo Sternberg, Jochen Brüning
    Pages 173-188
  13. Back Matter
    Pages 189-229

About this book

Introduction

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

Authors and affiliations

  • Victor W. Guillemin
    • 1
  • Shlomo Sternberg
    • 2
  • Jochen Brüning
    • 3
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät IIHumboldt-Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03992-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08433-1
  • Online ISBN 978-3-662-03992-2
  • Buy this book on publisher's site