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Fibre Bundles

Author: Dale Husemoller
Publisher: New York, NY : Springer New York, 1994.
Series: Graduate texts in mathematics, 20.
Edition/Format:   eBook : Document : English : Third editionView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Dale Husemoller
ISBN: 9781475722611 1475722613
OCLC Number: 851734922
Description: 1 online resource (xix, 355 pages).
Contents: 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.
Series Title: Graduate texts in mathematics, 20.
Responsibility: by Dale Husemoller.

Abstract:

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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