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Guillemin V., Sternberg S. — Supersymmetry and Equivariant de Rham Theory
Guillemin V., Sternberg S. — Supersymmetry and Equivariant de Rham Theory

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Название: Supersymmetry and Equivariant de Rham Theory

Авторы: Guillemin V., Sternberg S.


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. Brning 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.

Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 228

Добавлена в каталог: 16.04.2005

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Предметный указатель
$d_G$      45 55
$G^*$ algebra      17
$G^*$ module      17
$G^*$ morphism      18
Basic cohomology      26
Basic elements      26
Basic subcomplex      26 54
Berezin integral      78
Berezin integration      77
Bianchi identity      36 38
Borel's theorem      125
Canonical equivariant three-form      135
Cartan model      45
Cartan operator      45 55
Cartan structure equation      36
Cartan structure equations      38
Cartan's formula      58
Cartan's theorem      45
Chain homotopy      20
Chain homotopy relative to a morphism      22
Characteristic classes      95
Characteristic homomorphism      38 48 50
Chem — Weil map      38 48
Chern classes      97
Classifying bundle      4
Classifying space      4
Coadjoint orbits      114
Cohomology of flag varieties      125
Cohomology of toric varieties      126
Commutative superalgebra      13
Commutator      13
Connection elements      24
Connection forms      23
Curvature elements      24
Curvature forms      24
Delzant spaces      126
Derivation      14
Derivation, even      10
Derivation, odd      10
Double complex      61
Equivariant Characteristic Classes      104
Equivariant Chern classes      104
Equivariant Duistermaat — Heckman      133
equivariant Euler class      104
Equivariant Maxsden — Weinstein      132
Equivariant Pontryagin classes      104
Equivariant symplectic form      112 132
Euler class      98
Fermionic integral      78
Fermionic integration      77
Flag manifolds      124
Gaussian Integrals      79
Hamiltonian homogeneous spaces      114
Horizontal bundle      23
Horizontal form      23
Kirillov — Kostant — Souriau theorem      114
Koszul complex      33
Kuiper      6
Lie derivative      10
Lie superalgebra      13
Lie superalgebra, g      14
Locally free action      23
Marsden — Weinstein reduction      118
Marsden — Weinstein theorem      118
Mathai — Quillen isomorphism      42
Minimal coupling form      117
Moment map      112
Pfaffian      97
Pontryagin classes      97
Quillen's law      12
Splitting manifold      107
Splitting principle      74 106
Structure constants      9
Summation convention      9
Super Fourier transform      90
Super Jacobi identity      13
Superalgebra      12
Supercommutator      13
Supervector space      11
Symplectic reduction      119
Tensor product of superalgebras      15
The Weil algebra      34
Total Chern class      101
Total complex      61
Type (C)      24
Universal Thom form      86 88
Vector field corresponding to $\xi$      10
Weil identities      11
Weil model      45
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