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Connections, curvature, and cohomology . Volume 3 Cohomology of principal bundles and homogeneous spaces [[electronic resource] /] / Werner Greub, Stephen Halperin, and Ray Vanstone



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Autore: Greub Werner Hildbert <1925-> Visualizza persona
Titolo: Connections, curvature, and cohomology . Volume 3 Cohomology of principal bundles and homogeneous spaces [[electronic resource] /] / Werner Greub, Stephen Halperin, and Ray Vanstone Visualizza cluster
Pubblicazione: New York, : Academic Press, 1976
Descrizione fisica: 1 online resource (617 p.)
Disciplina: 516.36
Soggetto topico: Connections (Mathematics)
Curvature
Homology theory
Soggetto genere / forma: Electronic books.
Altri autori: HalperinStephen  
VanstoneRay  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographies.
Nota di contenuto: Cover; Contents; Introduction; 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 theorems5. 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 groupsChapter 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 Bundles1. 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 pairs5. 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
Sommario/riassunto: Imidazole and Benzimidazole Synthesis is a comprehensive survey of the known methods of syntheses and ring modification. It brings together the multitude of synthesis of the imidazole ring in a systemic way interms of specific bond formation, and recommends the most attractive synthetic approaches. It also collects non-ring-synthetic approaches to classes of compounds such as nitro-, halogeno-, and amino-imidazoles, and covers the synthesis of N-substituted compounds and preparations of specific isomers.
Titolo autorizzato: Connections, curvature, and cohomology  Visualizza cluster
ISBN: 1-281-46686-7
9786611466862
0-08-087927-6
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910307293603321
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