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BL
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| Record Number
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970573
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b724943
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| Main Entry
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Mahammed, N.,1944-
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| Title & Author
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Some applications of topological K-theory\ N. Mahammed, R. Piccinini, U. Suter.
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| Publication Statement
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Amsterdam ;New York :: North-Holland Pub. Co. :New York :: sole distributors for the U.S.A. and Canada, Elsevier North-Holland,, 1980.
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| Series Statement
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North-Holland mathematics studies ;; 45
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Notas de matemática ;; 74
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| Page. NO
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1 online resource (329 p.).
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| ISBN
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0080871569
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: 1281797235
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: 6611797238
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: 9780080871561
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: 9781281797230
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: 9786611797232
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| Notes
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Description based upon print version of record.
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| Bibliographies/Indexes
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Includes bibliographical references (p. 295-314) and index.
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| Contents
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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
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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
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| Abstract
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Some applications of topological K-theory.
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| Subject
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Geometry, Algebraic.
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| Subject
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K-theory.
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Geometry, Algebraic.
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K-theory.
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| Dewey Classification
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510 s 514/.23 19510 s514.23512.55
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| LC Classification
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QA612.33.M34 1980
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| Added Entry
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Piccinini, Renzo A.,1933-
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Suter, U.,1935-
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