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Vector Bundles: Foundations and Stiefel–Whitney Classes Copyright Page Contents Preface Introduction Chapter I. Base Spaces 0. Introduction 1. The Category of Base Spaces 2. Some Simplicial Spaces 3. More Simplicial Spaces 4. Weak Simplicial Spaces 5. CW Spaces 6. Smooth Manifolds 7. Grassmann Manifolds 8. Some More Coverings 9. The Mayer–Vietoris Technique 10. Remarks and Exercises Chapter II. Fiber Bundles 0. Introduction 1. Fibre Bundles and Fiber Bundles 2. Coordinate Bundles 3. Bundles over Contractible Spaces 4. Pullbacks along Homotopic Maps 5. Reduction of Structure Groups 6. Polar Decompositions 7. The Leray–Hirsch Theorem 8. Remarks and Exercises Chapter III. Vector Bundles 0. Introduction 1. Real Vector Bundles 2. Whitney Sums and Products 3. Riemannian Metrics 4. Sections of Vector Bundles 5. Smooth Vector Bundles 6. Vector Fields and Tangent Bundles 7. Canonical Vector Bundles 8. The Homotopy Classification Theorem 9. More Smooth Vector Bundles 10. Orientable Vector Bundles 11. Complex Vector Bundles 12. Realifications and Complexifications 13. Remarks and Exercises Chapter IV. Z/2 Euler Classes 0. Introduction 1. The Z/2 Thom Class Uξ ε Hn(E, E*) 2. Properties of Z/2

Who reads Vector Bundles. Volume 1: Foundations and Stiefel-Whitney Classes (Pure and Applied Mathematics (Academic Pr))?

Author

Howard Osborn; ScienceDirect (Online service)

Publisher

Academic Press, Incorporated

Published

1983

Language

EN

ISBN

9781281768780

Category

nonfiction

Subjects

Mathematics, Stem