Supersymmetry and equivariant de Rham theory

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Supersymmetry and equivariant de Rham theory / Victor W. Guillemin, Shlomo Sternberg

資料種別:

図書

出版情報:

Berlin : Springer, 1999

形態:

xxiii, 228 p. ; 25 cm

著者名:

ISBN:

9783540647973 [354064797X]

書誌ID:

BA41242809

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Homology theory; Supersymmetry

言語:

英語

目次情報:

Introduction

Equivariant Cohomology in Topology / 1：

Equivariant Cohomology via Classifying Bundles / 1.1：

Existence of Classifying Spaces / 1.2：

Bibliographical Notes for Chapter 1 / 1.3：

G* Modules / 2：

Differential-Geometric Identities / 2.1：

The Language of Superalgebra / 2.2：

From Geometry to Algebra / 2.3：

Cohomology / 2.3.1：

Acyclicity / 2.3.2：

Chain Homotopies / 2.3.3：

Free Actions and the Condition (C) / 2.3.4：

The Basic Subcomplex / 2.3.5：

Equivariant Cohomology of G* Algebras / 2.4：

The Equivariant de Rham Theorem / 2.5：

Bibliographical Notes for Chapter 2 / 2.6：

The Weil Algebra / 3：

The Koszul Complex / 3.1：

Classifying Maps / 3.2：

W* Modules / 3.4：

Bibliographical Notes for Chapter 3 / 3.5：

The Weil Model and the Cartan Model / 4：

The Mathai-Quillen Isomorphism / 4.1：

The Cartan Model / 4.2：

Equivariant Cohomology of W* Modules / 4.3：

H ((A ⊗ E)_bas) does not depend on E / 4.4：

The Characteristic Homomorphism / 4.5：

Commuting Actions / 4.6：

The Equivariant Cohomology of Homogeneous Spaces / 4.7：

Exact Sequences / 4.8：

Bibliographical Notes for Chapter 4 / 4.9：

Cartan's Formula / 5：

The Cartan Model for W* Modules / 5.1：

Bibliographical Notes for Chapter 5 / 5.2：

Spectral Sequences / 6：

Spectral Sequences of Double Complexes / 6.1：

The First Term / 6.2：

The Long Exact Sequence / 6.3：

Useful Facts for Doing Computations / 6.4：

Functorial Behavior / 6.4.1：

Gaps / 6.4.2：

Switching Rows and Columns / 6.4.3：

The Cartan Model as a Double Complex

H_G(A) as an S(g*)^G-Module

Morphisms of G* Modules

Restricting the Group

Bibliographical Notes for Chapter 6 / 6.5：

Fermionic Integration / 7：

Definition and Elementary Properties / 7.1：

Integration by Parts / 7.1.1：

Change of Variables / 7.1.2：

Gaussian Integrals / 7.1.3：

Iterated Integrals / 7.1.4：

The Fourier Transform / 7.1.5：

The Mathai-Quillen Construction

The Fourier Transform of the Koszul Complex / 7.2：

Bibliographical Notes for Chapter 7 / 7.3：

Characteristic Classes / 8：

Vector Bundles / 8.1：

The Invariants / 8.2：

G = U(n) / 8.2.1：

G = O(n) / 8.2.2：

G = SO(2n) / 8.2.3：

Relations Between the Invariants / 8.3：

Restriction from U(n) to O(n) / 8.3.1：

Restriction from SO(2n) to U(n) / 8.3.2：

Restriction from U(n) to U(k) × U(ℓ) / 8.3.3：

Symplectic Vector Bundles / 8.4：

Consistent Complex Structures / 8.4.1：

Characteristic Classes of Symplectic Vector Bundles / 8.4.2：

Equivariant Characteristic Classes / 8.5：

Equivariant Chern classes / 8.5.1：

Equivariant Characteristic Classes of a Vector Bundle Over a Point / 8.5.2：

Equivariant Characteristic Classes as Fixed Point Data / 8.5.3：

The Splitting Principle in Topology

Bibliographical Notes for Chapter 8

Equivariant Symplectic Forms / 9：

Equivariantly Closed Two-Forms / 9.1：

The Case M = G / 9.2：

Equivariantly Closed Two-Forms on Homogeneous Spaces / 9.3：

The Compact Case / 9.4：

Minimal Coupling / 9.5：

Symplectic Reduction / 9.6：

The Duistermaat-Heckman Theorem / 9.7：

The Cohomology Ring of Reduced Spaces / 9.8：

Flag Manifolds / 9.8.1：

Delzant Spaces / 9.8.2：

Reduction: The Linear Case / 9.8.3：

Equivariant Duistermaat-Heckman

Group Valued Moment Maps

The Canonical Equivariant Closed Three-Form on G / 9.10.1：

The Exponential Map / 9.10.2：

G-Valued Moment Maps on Hamiltonian G-Manifolds / 9.10.3：

Conjugacy Classes / 9.10.4：

Bibliographical Notes for Chapter 9 / 9.11：

The Thom Class and Localization / 10：

Fiber Integration of Equivariant Forms / 10.1：

The Equivariant Normal Bundle / 10.2：

Modifying ν / 10.3：

Verifying that τ is a Thom Form / 10.4：

The Thom Class and the Euler Class / 10.5：

The Fiber Integral on Cohomology / 10.6：

Push-Forward in General / 10.7：

Localization / 10.8：

The Localization for Torus Actions / 10.9：

Bibliographical Notes for Chapter 10 / 10.10：

The Abstract Localization Theorem / 11：

Relative Equivariant de Rham Theory / 11.1：

Mayer-Vietoris / 11.2：

S(g*) Modules / 11.3：

The Chang-Skjelbred Theorem / 11.4：

Some Consequences of Equivariant Formality / 11.6：

Two Dimensional G-Manifolds / 11.7：

A Theorem of Goresky-Kottwitz-Mac Pherson / 11.8：

Bibliographical Notes for Chapter 11 / 11.9：

Appendix

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

Bibliography

Index

Introduction

Equivariant Cohomology in Topology / 1：

Equivariant Cohomology via Classifying Bundles / 1.1：

Existence of Classifying Spaces / 1.2：

Bibliographical Notes for Chapter 1 / 1.3：

G* Modules / 2：

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