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AuthorGuillemin, Victor W. author
TitleSupersymmetry and Equivariant de Rham Theory [electronic resource] / by Victor W. Guillemin, Shlomo Sternberg, Jochen Brรผning
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
Connect tohttp://dx.doi.org/10.1007/978-3-662-03992-2
Descript XXIII, 232 p. online resource

SUMMARY

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. Brรผning 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


CONTENT

1 Equivariant Cohomology in Topology -- 3 The Weil Algebra -- 4 The Weil Model and the Cartan Model -- 5 Cartanโ{128}{153}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 dโ{128}{153}algรจbre diffรฉrentielle; application aux groupes de Lie et aux variรฉtรฉs oรน opรจre un groupe de Lie: Henri Cartan -- La transgression dans un groupe de Lie et dans un espace fibrรฉ principal: Henri Cartan


Mathematics Differential geometry Algebraic topology Physics Mathematics Algebraic Topology Differential Geometry Theoretical Mathematical and Computational Physics



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