Supersymmetry and Equivariant de Rham Theory

Jochen Brüning, Professor für Mathematik an der Humboldt-Universität zu Berlin, ist Gründungsdirektor des Augsburger Instituts für Europäische Kulturgeschichte und Geschäftsführender Direktor des Hermann von Helmholtz-Zentrums für Kulturtechnik in Berlin.

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.

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."