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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
| Connections, curvature, and cohomology . Volume 3 Cohomology of principal bundles and homogeneous spaces [[electronic resource] /] / Werner Greub, Stephen Halperin, and Ray Vanstone |
| Autore | Greub Werner Hildbert <1925-> |
| Pubbl/distr/stampa | New York, : Academic Press, 1976 |
| Descrizione fisica | 1 online resource (617 p.) |
| Disciplina | 516.36 |
| Altri autori (Persone) |
HalperinStephen
VanstoneRay |
| Soggetto topico |
Connections (Mathematics)
Curvature Homology theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-46686-7
9786611466862 0-08-087927-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910307293603321 |
Greub Werner Hildbert <1925->
|
||
| New York, : Academic Press, 1976 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Connections, curvature, and cohomology . Volume 2 Lie groups, principal bundles, and characteristic classes [[electronic resource] /] / [by] Werner Greub, Stephen Halperin, and Ray Vanstone
| Connections, curvature, and cohomology . Volume 2 Lie groups, principal bundles, and characteristic classes [[electronic resource] /] / [by] Werner Greub, Stephen Halperin, and Ray Vanstone |
| Autore | Greub Werner Hildbert <1925-> |
| Pubbl/distr/stampa | New York, : Academic Press, 1973 |
| Descrizione fisica | 1 online resource (567 p.) |
| Disciplina |
510.8
514.2 516.36 |
| Altri autori (Persone) |
HalperinStephen
VanstoneRay |
| Collana | Pure and applied mathematics (Academic Press) |
| Soggetto topico |
Connections (Mathematics)
Curvature Homology theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-74393-3
9786611743932 0-08-087361-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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
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 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 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 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 |
| Record Nr. | UNINA-9910307304803321 |
|
Greub Werner Hildbert <1925->
|
||
| New York, : Academic Press, 1973 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Connections, curvature, and cohomology . Volume 1 De Rham cohomology of manifolds and vector bundles [[electronic resource] /] / [by] Werner Greub, Stephen Halperin, and Ray Vanstone
| Connections, curvature, and cohomology . Volume 1 De Rham cohomology of manifolds and vector bundles [[electronic resource] /] / [by] Werner Greub, Stephen Halperin, and Ray Vanstone |
| Autore | Greub Werner Hildbert <1925-> |
| Pubbl/distr/stampa | New York, : Academic Press, 1972 |
| Descrizione fisica | 1 online resource (467 p.) |
| Disciplina |
510.8 s514.2
510/.8 s 514/.2 514.23 |
| Altri autori (Persone) |
HalperinStephen
VanstoneRay |
| Collana |
Pure and applied mathematics; a series of monographs and textbooks
Connections, curvature, and cohomology |
| Soggetto topico |
Connections (Mathematics)
Homology theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-76355-1
9786611763558 0-08-087360-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Connections, Curvature, and Cohomology; Copyright Page; Contents; Preface; Introduction; Contents of Volumes II and III; Chapter 0. Algebraic and Analytic Preliminaries; 1. Linear algebra; 2. Homological algebra; 3. Analysis and topology; Chapter I. Basic Concepts; 1. Topological manifolds; 2. Smooth manifolds; 3. Smooth fibre bundles; Problems; Chapter II. Vector Bundles; 1. Basic concepts; 2. Algebraic operations with vector bundles; 3. Cross-sections; 4. Vector bundles with extra structure; 5. Structure theorems; Problems; Chapter III. Tangent Bundle and Differential Forms
1. Tangent bundle2. Local properties of smooth maps; 3. Vector fields; 4. Differential forms; 5. Orientation; Problems; Chapter IV. Calculus of Differential Forms; 1. The Opertors i,?,d; 2. Smooth families of differential forms; 3. Integration of n-forms; 4. Stokes' theorem; Problems; Chapter V. De Rham Cohomology; 1. The axioms; 2. Examples; 3. Cohomology with compact supports; 4. Poincaré duality; 5. Applications of Poincaré duality; 6. Kiinneth theorems; 7. The De Rham theorem; Problems; Chapter VI. Mapping Degree; 1. Global degree; 2. The canonical map aM; 3. Local degree 4. The Hopf theoremProblems; Chapter VII. Integration over the Fibre; 1. Tangent bundle of a fibre bundle; 2. Orientation in fibre bundles; 3. Vector bundles and sphere bundles; 4. Fibre-compact carrier; 5. Integration over the fibre; Problems; Chapter VIII. Cohomology of Sphere Bundles; 1. Euler class; 2. The difference class; 3. Index of a cross-section at an isolated singularity; 4. Index sum and Euler class; 5. Existence of cross-sections in a sphere bundle; Problems; Chapter IX. Cohomology of Vector Bundles; 1. The Thom isomorphism; 2. The Thom class of a vector bundle 3. Index of a cross-section at an isolated zeroProblems; Chapter X. The Lefschetz Class of a Manifold; I . The Lefschetz isomorphism; 2. Coincidence number; 3. The Lefschetz coincidence theorem; Problems; Appendix A. The Exponential Map; References; Bibliography; Bibliography-Books; Notation Index; Index; Pure and Applied Mathematics |
| Record Nr. | UNINA-9910307303303321 |
|
Greub Werner Hildbert <1925->
|
||
| New York, : Academic Press, 1972 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||