دانلود کتاب Connections, Curvature, and Cohomology. Vol. III: Cohomology of principal bundles and homogeneous spaces (Pure and Applied Mathematics Series; v. 47-III)

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Front Cover
Connections, Curvature, and Cohomology
Copyright Page
Contents
Preface
Introduction
Contents of Volumes I and II
Chapter 0. Algebraic Preliminaries
PART 1
Chapter I. Spectral Sequences
1. Filtrations
2. Spectral sequences
3. Graded filtered differential spaces
4. Graded filtered differential algebras
5. Differential couples
Chapter II. Koszul Complexes of P-Spaces and P-Algebras
1. P-spaces and P-algebras
2. Isomorphism theorems
3. The Poincaré–Koszul series
4. Structure theorems
5. Symmetric P-algebras
6. Essential P-algebras
Chapter III. Koszul Complexes of P-Differential Algebras
1. P-differential algebras
2. Tensor difference
3. Isomorphism theorems
4. Structure theorems
5. Cohomology diagram of a tensor difference
6. Tensor difference with a symmetric P-algebra
7. Equivalent and c-equivalent (P, d)-algebras
PART 2
Chapter IV. Lie Algebras and Differential Spaces
1. Lie algebras
2. Representation of a Lie algebra in a differential space
Chapter V. Cohomology of Lie Algebras and Lie Groups
1. Exterior algebra over a Lie algebra
2. Unimodular Lie algebras
3. Reductive Lie algebras
4. The structure theorem for (.E). =0
5. The structure of (.E*).=0
6. Duality theorems
7. Cohomology with coefficients in a graded Lie module
8. Applications to Lie groups
Chapter VI. The Weil Algebra
1. The Weil algebra
2. The canonical map PE
3. The distinguished transgression
4. The structure theorem for (VE*).=0
5. The structure theorem for (VE).=0, and duality
6. Cohomology of the classical Lie algebras
7. The compact classical Lie groups
Chapter VII. Operation of a Lie Algebra in a Graded Differential Algebra
1. Elementary properties of an operation
2. Examples of operations
3. The structure homomorphism
4. Fibre projection
5. Operation of a graded vector space on a graded algebra
6. Transformation groups
Chapter VIII. Algebraic Connections and Principal Bundles
1. Definition and examples
2. The decomposition of R
3. Geometric definition of an operation
4. The Weil homomorphism
5. Principal bundles
Chapter IX. Cohomology of Operations and Principal Bundles
1. The filtration of an operation
2. The fundamental theorem
3. Applications of the fundamental theorem
4. The distinguished transgression
5. The classification theorem
6. Principal bundles
7. Examples
Chapter X. Subalgebras
1. Operation of a subalgebra
2. The cohomology of (.E*)iF=0,.F=0
3. The structure of the algebra H(E/F)
4. Cartan pairs
5. Subalgebras noncohomologous to zero
6. Equal rank pairs
7. Symmetric pairs
8. Relative Poincaré duality
9. Symplectic metrics
Chapter XI. Homogeneous Spaces
1. The cohomology of a homogeneous space
2. The structure of H(G/K)
3. The Weyl group
4. Examples of homogeneous spaces
5. Non-Cartan pairs
Chapter XII. Operation of a Lie Algebra Pair
1. Basic properties
2. The cohomology of BF
3. Isomorphism of the cohomology diagrams
4. Applications of the fundamental theorem
5. Bundles with fibre a homogeneous space
Appendix A. Characteristic Coefficients and the Pfaffian
1. Characteristic and trace coefficients
2. Inner product spaces
Notes
References
Bibliography
Index