Some Applications of Topological K-Theory (eBook)

eBook Download: PDF

1980 | 1. Auflage
316 Seiten
Elsevier Science (Verlag)
978-0-08-087156-1 (ISBN)

Infos

Some applications of topological K-theory

Inhalt

Front Cover 1
Some Applications of Topological K-Theory 4
Copyright Page 5
Table of Contents 8
Preface 6
Chapter 0. A Review of K - Theory 12
Chapter 1. The Hopf Invariant 24
1. Introduction 24
2. The Hopf Invariant of Maps from S3 onto S2 25
3. The Hopf Invariant of Maps f : S2n-1 . Sn 36
4. Cohomological Interpretation of the Hopf Invariant 41
5. K – Theoretical Solution of the Hopf Invariant One Problem and Applications 47
Chapter 2. Torsion Free H – Spaces of Rank Two 54
1. Introduction 54
2. Hopf Construction, projective Plane and Type of Torsion free Rank two H - spaces 57
3. Torsion free H – spaces of Type (3,7) 65
4. The Homotopy Type Classification 74
5. K - Theoretical Proof of the Type Classification Theorem 83
Chapter 3. Homotopy and Stably Complex Structure 92
1. The Question of Complex Structure 92
2. Almost Complex Manifolds and Stably Complex Manifolds 94
3. The Homotopy Type of M and M 98
4. The manifold is not stably complex 101
Chapter 4. Vector Fields on Spheres 104
1. Introduction 104
2. Vector Fields and Sphere Bundles over Projective Spaces 108
3. The K - Theory of the projective Spaces 117
4. Real Vector Fields on Spheres 130
5. Cross-Sections of Complex Stiefel Fibrations 134
6. Cross-Sections of Quaternionic Stiefel Fibrations 141
Chapter 5. Span of Spherical Forms 150
1. Introduction and Generalities about Spherical Forms 150
2. Vector Fields on Spherical Forms 157
3. G – Fibre Homotopy J – Equivalence 163
4. G – (Co) Reducibility 171
5. Span of Spherical Forms of Cyclic Type 179
6. Span of Spherical Forms of Quaternionic Type 184
Chapter 6. Immersions and Embeddings of Manifolds 188
1. Background 188
2. A brief Historical Survey 193
3. Atiyah’s Criterion 199
4. About Immersions and Embeddings of Lens Spaces 209
5. The Case of the Qm – Spherical Forms 217
6. Parallelizability of the Spherical Forms 223
7. Immersions of Complex Projective Spaces 228
Chapter 7. Group Homomorphisms and Maps Between Classifying Spaces Vector Bundles Over Suspensions
1. Generalities 236
2. Cartan-Serre-Whitehead Towers and H – Spaces 237
3. Remarks about the KU – Theory of certain Classifying Spaces 240
4. A Theorem of Non-Surjectivity for aG,H 243
5. Vector Bundles over Suspensions 245
Chapter 8. On the Index Theorem of Elliptic Operators 250
1. Introduction 250
2. The Index of an Elliptic Differential Operator 255
3. Four Standard Complexes 265
4. The Index Theorem 278
5. The Generalized Lefschetz Fixed-Point Formula 292
Bibliography 306
Index 326

Produkt-Details

• Erscheint lt. Verlag: 1.1.1980
• Mitarbeit: Herausgeber (Serie): N. Mahammed, R. Piccinini, U. Suter
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-087156-9 / 0080871569
• ISBN-13: 978-0-08-087156-1 / 9780080871561