Some Applications of Topological K-Theory

Name: Some Applications of Topological K-Theory
Brand: Elsevier
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Elsevier (Verlag)

Erschienen am 1. Januar 1980

316 Seiten

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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

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