UID:
edoccha_9958085669802883
Umfang:
1 online resource (567 p.)
ISBN:
1-281-74393-3
,
9786611743932
,
0-08-087361-8
Serie:
Pure and applied mathematics (Academic Press) ; v. 47
Inhalt:
Spectral Theory of Random Matrices
Anmerkung:
Description based upon print version of record.
,
Front Cover; Connections, Curvature, and Cohomology, Volume II; Copyright Page; Contents; Preface; Introduction; Contents of Volumes I and III; Chapter 0. Algebraic and Analytic Preliminaries; 1. Linear algebra; 2. Homological algebra; 3. Analysis and topology; 4. Summary of volume I; Chapter I. Lie Groups; 1. Lie algebra of a Lie group; 2. The exponential map; 3. Representations; 4. Abelian Lie groups; 5. Integration on compact Lie groups; Problems; Chapter II. Subgroups and Homogeneous Spaces; 1. Lie subgroups; 2. Linear groups; 3. Homogeneous spaces
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4. The bundle structure of a homogeneous space5. Maximal tori; Problems; Chapter III. Transformation Groups; 1. Action of a Lie group; 2. Orbits of an action; 3. Vector fields; 4. Differential forms; 5. Invariant cross-sections; Problems; Chapter IV. Invariant Cohomology; 1. Group actions; 2. Left invariant forms on a Lie group; 3. Invariant cohomology of Lie groups; 4. Cohomology of compact connected Lie groups; 5. Homogeneous spaces; Problems; Chapter V. Bundles with Structure Group; 1. Principal bundles; 2. Associated bundles; 3. Bundles and homogeneous spaces; 4. The Grassmannians
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5. The Stiefel manifolds6. The cohomology of the Stiefel manifolds and the classical groups; Problems; Chapter VI. Principal Connections and the Weil Homomorphism; 1. Vector fields; 2. Differential forms; 3. Principal connections; 4. The covariant exterior derivative; 5. Curvature; 6. The Weil homomorphism; 7. Special cases; 8. Homogeneous spaces; Problems; Chapter VII. Linear Connections; 1. Bundle-valued differential forms; 2. Examples; 3. Linear connections; 4. Curvature; 5. Parallel translation; 6. Horizontal subbundles; 7. Riemannian connections; 8. Sphere maps; Problems
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Chapter VIII. Characteristic Homomorphism for E-bundles1. E-bundles; 2. E-connections; 3. Invariant subbundles; 4. Characteristic homomorphism; 5. Examples; 6. E-bundles with compact carrier; 7. Associated principal bundles; 8. Characteristic homomorphism for associated vector bundles; Problems; Chapter IX. Pontrjagin, Pfaffian, and Chern Classes; 1. The modified characteristic homomorphism for real E-bundles; 2. Real bundles: Pontrjagin and trace classes; 3. Pseudo-Riemannian bundles: Pontrjagin classes and Pfaffian class; 4. Complex vector bundles; 5. Chern classes; Problems
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Chapter X. The Gauss-Bonnet-Chern TheoremProblems; Appendix A. Characteristic Coefficients and the Pfaffian; 1. Characteristic and trace coefficients; 2. Inner product spaces; References; Bibliography; Chapters I-V; Chapters VI-X; Bibliography-Books; Notation Index; Index
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English
Weitere Ausg.:
ISBN 0-12-302702-0
Sprache:
Englisch
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