Fibre bundles
著者
書誌事項
Fibre bundles
（Graduate texts in mathematics, 20）
Springer-Verlag, c1994
3rd ed
- : us
- : gw
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注記
1st ed.: Published 1966, by McGraw-Hill, Inc
Bibliography: p. [339]-349
Includes index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387940878
内容説明
Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. The new edition of this text includes two additional chapters, one on the gauge group of a bundle and the other on the differential forms representing characteristic classes of complex vector bundles on manifolds.
目次
1 Preliminaries on Homotopy Theory.- I The General Theory of Fibre Bundles.- 2 Generalities on Bundles.- 3 Vector Bundles.- 4 General Fibre Bundles.- 5 Local Coordinate Description of Fibre Bundles.- 6 Change of Structure Group in Fibre Bundles.- 7 The Gauge Group of a Principal Bundle.- 8 Calculations Involving the Classical Groups.- II Elements of K-Theory.- 9 Stability Properties of Vector Bundles.- 10 Relative K-Theory.- 11 Bott Periodicity in the Complex Case.- 12 Clifford Algebras.- 13 The Adams Operations and Representations.- 14 Representation Rings of Classical Groups.- 15 The Hopf Invariant.- 16 Vector Fields on the Sphere.- III Characteristic Classes.- 17 Chern Classes and Stiefel-Whitney Classes.- 18 Differentiable Manifolds.- 19 Characteristic Classes and Connections.- 20 General Theory of Characteristic Classes.- Appendix 1 Dold's Theory of Local Properties of Bundles.- Appendix 2 On the Double Suspension.- 4. Single Suspension Sequences.- 7. Double Suspension Sequences.
- 巻冊次
-
: gw ISBN 9783540940876
内容説明
Fibre bundles play an important role in every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition, two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles.
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