04140nam 2200637Ia 450 991030730330332120170815144652.01-281-76355-197866117635580-08-087360-X(CKB)1000000000557122(EBL)404054(OCoLC)476217000(SSID)ssj0000389755(PQKBManifestationID)11257161(PQKBTitleCode)TC0000389755(PQKBWorkID)10448124(PQKB)11361366(MiAaPQ)EBC404054(EXLCZ)99100000000055712220720705d1972 uy 0engur|n|---|||||txtccrConnections, curvature, and cohomologyVolume 1De Rham cohomology of manifolds and vector bundles[electronic resource] /[by] Werner Greub, Stephen Halperin, and Ray VanstoneNew York Academic Press19721 online resource (467 p.)Pure and applied mathematics; a series of monographs and textbooks ;47Connections, curvature, and cohomology ;1Description based upon print version of record.0-12-302701-2 Includes bibliographies and index.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 Forms1. 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 degree4. 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 bundle3. 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 MathematicsConnections, curvature, and cohomology V1Pure and applied mathematics (Academic Press) ;47.Connections (Mathematics)Homology theoryElectronic books.Connections (Mathematics)Homology theory.510.8 s514.2510/.8 s 514/.2514.23Greub Werner Hildbert1925-47382Halperin Stephen47383Vanstone Ray47384MiAaPQBOOK9910307303303321Connections, curvature, and cohomology2151955UNINA