Ebook: Fibre Bundles

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Content:
Front Matter....Pages i-xv
Preliminaries on Homotopy Theory....Pages 1-8
Front Matter....Pages 9-9
Generalities on Bundles....Pages 11-22
Vector Bundles....Pages 23-38
General Fibre Bundles....Pages 39-58
Local Coordinate Description of Fibre Bundles....Pages 59-69
Change of Structure Group in Fibre Bundles....Pages 70-74
Calculations Involving the Classical Groups....Pages 75-95
Front Matter....Pages 97-97
Stability Properties of Vector Bundles....Pages 99-109
Relative K-Theory....Pages 110-127
Bott Periodicity in the Complex Case....Pages 128-138
Clifford Algebras....Pages 139-158
The Adams Operations and Representations....Pages 159-175
Representation Rings of Classical Groups....Pages 176-195
The Hopf Invariant....Pages 196-202
Vector Fields on the Sphere....Pages 203-228
Front Matter....Pages 229-229
Chern Classes and Stiefel-Whitney Classes....Pages 231-247
Differentiable Manifolds....Pages 248-265
General Theory of Characteristic Classes....Pages 266-283
Back Matter....Pages 285-327

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Content:
Front Matter....Pages i-xv
Preliminaries on Homotopy Theory....Pages 1-8
Front Matter....Pages 9-9
Generalities on Bundles....Pages 11-22
Vector Bundles....Pages 23-38
General Fibre Bundles....Pages 39-58
Local Coordinate Description of Fibre Bundles....Pages 59-69
Change of Structure Group in Fibre Bundles....Pages 70-74
Calculations Involving the Classical Groups....Pages 75-95
Front Matter....Pages 97-97
Stability Properties of Vector Bundles....Pages 99-109
Relative K-Theory....Pages 110-127
Bott Periodicity in the Complex Case....Pages 128-138
Clifford Algebras....Pages 139-158
The Adams Operations and Representations....Pages 159-175
Representation Rings of Classical Groups....Pages 176-195
The Hopf Invariant....Pages 196-202
Vector Fields on the Sphere....Pages 203-228
Front Matter....Pages 229-229
Chern Classes and Stiefel-Whitney Classes....Pages 231-247
Differentiable Manifolds....Pages 248-265
General Theory of Characteristic Classes....Pages 266-283
Back Matter....Pages 285-327
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