UID:
almahu_9947367855302882
Format:
1 online resource (329 p.)
ISBN:
1-281-79723-5
,
9786611797232
,
0-08-087156-9
Series Statement:
North-Holland mathematics studies ; 45
Content:
Some applications of topological K-theory
Note:
Description based upon print version of record.
,
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
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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
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6. Cross-Sections of Quaternionic Stiefel FibrationsChapter 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
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7. Immersions of Complex Projective SpacesChapter 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
,
English
Additional Edition:
ISBN 0-444-86113-0
Language:
English
