Some Applications of Topological K-Theory
Elsevier (Publisher)
Published on 1. January 1980
316 pages
978-0-08-087156-1 (ISBN)
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Some Applications of Topological K-Theory
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Some Applications of Topological K-Theory
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11/1980
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Content
- Front Cover
- Some Applications of Topological K-Theory
- Copyright Page
- Table of Contents
- Preface
- Chapter 0. A Review of K - Theory
- Chapter 1. The Hopf Invariant
- 1. Introduction
- 2. The Hopf Invariant of Maps from S3 onto S2
- 3. The Hopf Invariant of Maps f : S2n-1 Sn
- 4. Cohomological Interpretation of the Hopf Invariant
- 5. K - Theoretical Solution of the Hopf Invariant One Problem and Applications
- Chapter 2. Torsion Free H - Spaces of Rank Two
- 1. Introduction
- 2. Hopf Construction, projective Plane and Type of Torsion free Rank two H - spaces
- 3. Torsion free H - spaces of Type (3,7)
- 4. The Homotopy Type Classification
- 5. K - Theoretical Proof of the Type Classification Theorem
- Chapter 3. Homotopy and Stably Complex Structure
- 1. The Question of Complex Structure
- 2. Almost Complex Manifolds and Stably Complex Manifolds
- 3. The Homotopy Type of M and M
- 4. The manifold is not stably complex
- Chapter 4. Vector Fields on Spheres
- 1. Introduction
- 2. Vector Fields and Sphere Bundles over Projective Spaces
- 3. The K - Theory of the projective Spaces
- 4. Real Vector Fields on Spheres
- 5. Cross-Sections of Complex Stiefel Fibrations
- 6. Cross-Sections of Quaternionic Stiefel Fibrations
- Chapter 5. Span of Spherical Forms
- 1. Introduction and Generalities about Spherical Forms
- 2. Vector Fields on Spherical Forms
- 3. G - Fibre Homotopy J - Equivalence
- 4. G - (Co) Reducibility
- 5. Span of Spherical Forms of Cyclic Type
- 6. Span of Spherical Forms of Quaternionic Type
- Chapter 6. Immersions and Embeddings of Manifolds
- 1. Background
- 2. A brief Historical Survey
- 3. Atiyah's Criterion
- 4. About Immersions and Embeddings of Lens Spaces
- 5. The Case of the Qm - Spherical Forms
- 6. Parallelizability of the Spherical Forms
- 7. Immersions of Complex Projective Spaces
- Chapter 7. Group Homomorphisms and Maps Between Classifying Spaces
- Vector Bundles Over Suspensions
- 1. Generalities
- 2. Cartan-Serre-Whitehead Towers and H - Spaces
- 3. Remarks about the KU - Theory of certain Classifying Spaces
- 4. A Theorem of Non-Surjectivity for aG,H
- 5. Vector Bundles over Suspensions
- Chapter 8. On the Index Theorem of Elliptic Operators
- 1. Introduction
- 2. The Index of an Elliptic Differential Operator
- 3. Four Standard Complexes
- 4. The Index Theorem
- 5. The Generalized Lefschetz Fixed-Point Formula
- Bibliography
- Index
