Ebook: Fibre Bundles

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Content:
Front Matter....Pages i-xix
Preliminaries on Homotopy Theory....Pages 1-8
Front Matter....Pages 9-9
Generalities on Bundles....Pages 11-23
Vector Bundles....Pages 24-39
General Fibre Bundles....Pages 40-60
Local Coordinate Description of Fibre Bundles....Pages 61-72
Change of Structure Group in Fibre Bundles....Pages 73-78
The Gauge Group of a Principal Bundle....Pages 79-86
Calculations Involving the Classical Groups....Pages 87-107
Front Matter....Pages 109-109
Stability Properties of Vector Bundles....Pages 111-121
Relative K-Theory....Pages 122-139
Bott Periodicity in the Complex Case....Pages 140-150
Clifford Algebras....Pages 151-170
The Adams Operations and Representations....Pages 171-188
Representation Rings of Classical Groups....Pages 189-209
The Hopf Invariant....Pages 210-216
Vector Fields on the Sphere....Pages 217-242
Front Matter....Pages 243-243
Chern Classes and Stiefel-Whitney Classes....Pages 245-261
Differentiable Manifolds....Pages 262-279
Characteristic Classes and Connections....Pages 280-293
General Theory of Characteristic Classes....Pages 294-311
Back Matter....Pages 312-355

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Content:
Front Matter....Pages i-xix
Preliminaries on Homotopy Theory....Pages 1-8
Front Matter....Pages 9-9
Generalities on Bundles....Pages 11-23
Vector Bundles....Pages 24-39
General Fibre Bundles....Pages 40-60
Local Coordinate Description of Fibre Bundles....Pages 61-72
Change of Structure Group in Fibre Bundles....Pages 73-78
The Gauge Group of a Principal Bundle....Pages 79-86
Calculations Involving the Classical Groups....Pages 87-107
Front Matter....Pages 109-109
Stability Properties of Vector Bundles....Pages 111-121
Relative K-Theory....Pages 122-139
Bott Periodicity in the Complex Case....Pages 140-150
Clifford Algebras....Pages 151-170
The Adams Operations and Representations....Pages 171-188
Representation Rings of Classical Groups....Pages 189-209
The Hopf Invariant....Pages 210-216
Vector Fields on the Sphere....Pages 217-242
Front Matter....Pages 243-243
Chern Classes and Stiefel-Whitney Classes....Pages 245-261
Differentiable Manifolds....Pages 262-279
Characteristic Classes and Connections....Pages 280-293
General Theory of Characteristic Classes....Pages 294-311
Back Matter....Pages 312-355
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