Fibre Bundles

Dale Husemoller (auth.)0387940871, 9780387940878

Fibre bundles play an important role in just about 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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Table of contents :
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