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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
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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
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Connections, curvature, and cohomology / Werner Greub, Stephen Halperin, and Ray Vanstone
Connections, curvature, and cohomology / Werner Greub, Stephen Halperin, and Ray Vanstone
Autore Greub, Werner Hildbert
Pubbl/distr/stampa New York : Academic Press, 1972-76
Descrizione fisica 3 v. ; 24 cm
Disciplina 514.23
516.36
Altri autori (Persone) Halperin, Stephenauthor
Vanstone, Ray
Collana Pure and applied mathematics. A series of monographs & textbooks, [Academic Press] 0079-8169 ; 47/I
Pure and applied mathematics. A series of monographs & textbooks, [Academic Press] 0079-8169 ; 47/II
Pure and applied mathematics. A series of monographs & textbooks, [Academic Press] 0079-8169 ; 47/III
Soggetto topico Connections
Curvature
Differential geometry
Homology theory
Classificazione AMS 53-XX
AMS 57-XX
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-b10756632
Greub, Werner Hildbert  
New York : Academic Press, 1972-76
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Lo trovi qui: Univ. del Salento
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Curvature : a variational approach / / A. Agrachev, D. Barilari, L. Rizzi
Curvature : a variational approach / / A. Agrachev, D. Barilari, L. Rizzi
Autore Agrachev A.
Pubbl/distr/stampa Providence, RI : , : American Mathematical Society, , [2018]
Descrizione fisica 1 online resource (v, 142 pages)
Disciplina 516.362
Collana Memoirs of the American Mathematical Society
Soggetto topico Curvature
Riemannian manifolds
Geometry, Differential
Soggetto genere / forma Electronic books.
ISBN 1-4704-4913-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910479865203321
Agrachev A.  
Providence, RI : , : American Mathematical Society, , [2018]
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Curvature : a variational approach / / A. Agrachev, D. Barilari, L. Rizzi
Curvature : a variational approach / / A. Agrachev, D. Barilari, L. Rizzi
Autore Agrachev A.
Pubbl/distr/stampa Providence, RI : , : American Mathematical Society, , [2018]
Descrizione fisica 1 online resource (v, 142 pages)
Disciplina 516.362
Collana Memoirs of the American Mathematical Society
Soggetto topico Curvature
Riemannian manifolds
Geometry, Differential
Soggetto genere / forma Electronic books.
ISBN 1-4704-4913-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910538812203321
Agrachev A.  
Providence, RI : , : American Mathematical Society, , [2018]
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Curvature and Betti Numbers. (AM-32), Volume 32 / / Kentaro Yano, Salomon Trust
Curvature and Betti Numbers. (AM-32), Volume 32 / / Kentaro Yano, Salomon Trust
Autore Trust Salomon
Pubbl/distr/stampa Princeton, NJ : , : Princeton University Press, , [2016]
Descrizione fisica 1 online resource (205 pages)
Disciplina 513.7
516.7*
Collana Annals of Mathematics Studies
Soggetto topico Curvature
Geometry, Differential
Soggetto genere / forma Electronic books.
Soggetto non controllato Abelian integral
Affine connection
Algebraic operation
Almost periodic function
Analytic function
Arc length
Betti number
Coefficient
Compact space
Complex analysis
Complex conjugate
Complex dimension
Complex manifold
Conservative vector field
Constant curvature
Constant function
Continuous function
Convex set
Coordinate system
Covariance and contravariance of vectors
Covariant derivative
Curvature
Derivative
Differential form
Differential geometry
Dimension (vector space)
Dimension
Einstein manifold
Equation
Euclidean domain
Euclidean geometry
Euclidean space
Existential quantification
Geometry
Hausdorff space
Hypersphere
Killing vector field
Kähler manifold
Lie group
Manifold
Metric tensor (general relativity)
Metric tensor
Mixed tensor
One-parameter group
Orientability
Partial derivative
Periodic function
Permutation
Quantity
Ricci curvature
Riemannian manifold
Scalar (physics)
Sectional curvature
Self-adjoint
Special case
Subset
Summation
Symmetric tensor
Symmetrization
Tensor algebra
Tensor calculus
Tensor field
Tensor
Theorem
Torsion tensor
Two-dimensional space
Uniform convergence
Uniform space
Unit circle
Unit sphere
Unit vector
Vector field
ISBN 1-4008-8220-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Preface -- Contents -- Chapter I. Riemannian Manifold -- Chapter II. Harmonic and Killing Vectors -- Chapter III. Harmonic and Killing Tensors -- Chapter IV. Harmonic and Killing Tensors in Flat Manifolds -- Chapter V. Deviation from Flatness -- Chapter VI. Semi-simple Group Spaces -- Chapter VII. Pseudo-harmonic Tensors and Pseudo-Killing Tensors in Metric Manifolds with Torsion -- Chapter VIII. Kaehler Manifold -- Chapter IX. Supplements / Bochner, S. -- Bibliography -- Backmatter
Record Nr. UNINA-9910154748603321
Trust Salomon  
Princeton, NJ : , : Princeton University Press, , [2016]
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Curvature and characteristic classes / Johan L. Dupont
Curvature and characteristic classes / Johan L. Dupont
Autore Dupont, Johan Louis
Pubbl/distr/stampa Berlin ; Heidelberg : Springer-Verlag, 1978
Descrizione fisica vii, 175 p. ; 25 cm.
Disciplina 514.72
Collana Lecture notes in mathematics, 0075-8434 ; 640
Soggetto topico Characteristic classes
Curvature
Differential forms
Invariants
ISBN 3540086633
Classificazione AMS 57R20
AMS 58A10
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-b10759360
Dupont, Johan Louis  
Berlin ; Heidelberg : Springer-Verlag, 1978
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Curvature and homology [[electronic resource] /] / Samuel I. Goldberg
Curvature and homology [[electronic resource] /] / Samuel I. Goldberg
Autore Goldberg Samuel I
Pubbl/distr/stampa New York, : Dover Publications, 1982
Descrizione fisica 1 online resource (335 p.)
Disciplina 516.3/62
Collana Pure and applied mathematics
Soggetto topico Curvature
Homology theory
Geometry, Riemannian
Soggetto genere / forma Electronic books.
ISBN 1-281-76631-3
9786611766313
0-08-087323-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; Curvature and Homology; Copyright Page; Contents; Preface; Notation Index; Introduction; CHAPTER I. RIEMANNIAN MANIFOLDS; 1.1 Differentiable manifolds; 1.2 Tensors; 1.3 Tensor bundles; 1.4 Differential forms; 1.5 Submanifolds; 1.6 Integration of differential forms; 1.7 Affine connections; 1.8 Bundle of frames; 1.9 Riemannian geometry; 1.10 Sectional curvature; 1.11 Geodesic coordinates; Exercises; CHAPTER II. TOPOLOGY OF DIFFERENTIABLE MANI- FOLDS; 2.1 Complexes; 2.2 Singular homology; 2.3 Stokes' theorem; 2.4 De Rham cohomology; 2.5 Periods
2.6 Decomposition theorem for compact Riemann surfaces2.7 The star isomorphism; 2.8 Harmonic forms. The operators d and ?; 2.9 Orthogonality relations; 2.10 Decomposition theorem for compact Riemannian manifolds; 2.11 Fundamental theorem; 2.12 Explicit expressions for d, d and ?; Exercises; CHAPTER III. CURVATURE AND HOMOLOGY OF RIEMANNIAN MANIFOLDS; 3.1 Some contributions of S. Bochner; 3.2 Curvature and betti numbers; 3.3 Derivations in a graded algebra; 3.4 Infinitesimal transformations; 3.5 The derivation ?(X); 3.6 Lie transformation groups; 3.7 Conformal transformations
3.8 Conformal transformations (continued)3.9 Conformally flat manifolds; 3.10 Affline collineations; 3.11 Projective transformations; Exercises; CHAPTER IV. COMPACT LIE GROUPS; 4.1 The Grassman algebra of a Lie group; 4.2 Invariant differential forms; 4.3 Local geometry of a compact semi-simple Lie group; 4.4 Harmonic forms on a compact semi-simple Lie group; 4.5 Curvature and betti numbers of a compact semi-simple Lie group G; 4.6 Determination of the betti numbers of the simple Lie groups; Exercises; CHAPTER V. COMPLEX MANIFOLDS; 5.1 Complex manifolds; 5.2 Almost complex manifolds
5.3 Local hermitian geometry5.4 The operators L and A; 5.5 Kaehler manifolds; 5.6 Topology of a Kaehler manifold; 5.7 Effective forms on an hermitian manifold; 5.8 Holomorphic maps. Induced structures; 5.9 Examples of Kaehler manifolds; Exercises; CHAPTER VI. CURVATURE AND HOMOLOGY OF KAEHLER MANIFOLDS; 6.1 Holomorphic curvature; 6.2 The effect of positive Ricci curvature; 6.3 Deviation from constant holomorphic curvature; 6.4 Kaehler-Einstein spaces; 6.5 Holomorphic tensor fields; 6.6 Complex parallelisable manifolds; 6.7 Zero curvature; 6.8 Compact complex parallelisable manifolds
6.9 A topological characterization of compact complex parallelisable manifolds6.10 d"-cohomology; 6.11 Complex imbedding; 6.12 Euler characteristic; 6.13 The effect of sufficiently many holomorphic differentials; 6.14 The vanishing theorems of Kodaira; Exercises; CHAPTER VII. GROUPS OF TRANSFORMATIONS OF KAEHLER AND ALMOST KAEHLER MANIFOLDS; 7.1 Infinitesimal holomorphic transformations; 7.2 Groups of holomorphic transformations; 7.3 Kaehler manifolds with constant Ricci scalar curvature; 7.4 A theorem on transitive groups of holomorphic transformations
7.5 Infinitesimal conformal transformations. Automorphisms
Record Nr. UNINA-9910307293003321
Goldberg Samuel I  
New York, : Dover Publications, 1982
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Curvature and homology / Samuel I. Goldberg
Curvature and homology / Samuel I. Goldberg
Autore Goldberg, Samuel I.
Pubbl/distr/stampa New York : Academic Press, 1962
Descrizione fisica 315 p. : ill. ; 24 cm.
Disciplina 516.36
Collana Pure and applied mathematics. A series of monographs & textbooks [Academic Press], 0079-8169 ; 11
Soggetto topico Curvature
Homology theory
Riemann surfaces
Classificazione AMS 58-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-b10759372
Goldberg, Samuel I.  
New York : Academic Press, 1962
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Degree theory of immersed hypersurfaces / / Harold Rosenberg, Graham Smith
Degree theory of immersed hypersurfaces / / Harold Rosenberg, Graham Smith
Autore Rosenberg H (Harold), <1941->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2020
Descrizione fisica 1 online resource (74 pages)
Disciplina 516.3/73
Collana Memoirs of the American Mathematical Society
Soggetto topico Topological degree
Riemannian manifolds
Hypersurfaces
Curvature
Soggetto genere / forma Electronic books.
ISBN 1-4704-6148-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910480893803321
Rosenberg H (Harold), <1941->  
Providence, Rhode Island : , : American Mathematical Society, , 2020
Materiale a stampa
Lo trovi qui: Univ. Federico II
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