Supersymmetry and Equivariant de Rham Theory

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 195o in the Proceedings of the "Colloque de Topologie". These papers are reproduced here, together with a scholarly introduction to the subject frorn 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 frorn the de Rham theoretic perspective. The well established topological approach is linked with the différential form aspect through the equivariant de Rham 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.