Supersymmetry and Equivariant de Rham Theory [Paperback]

This book discusses 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. It covers almost all important aspects of the subject The authors are key authorities in this field.

Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Br?ning 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.1 Equivariant Cohomology in Topology.- 3 The Weil Algebra.- 4 The Weil Model and the Cartan Model.- 5 Cartans 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 dalg?bre diff?rentielle; application aux groupes de Lie et aux vari?t?s o? op?re un groupe de Lie: Henri Cartan.- La transgression dans un groupe de Lie et dans un espace fibr? 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 understl3#