Overview

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.

Full Product Details

Author:   Dale Husemöller
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 3rd ed. 1994
Volume:   20
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   0.575kg
ISBN:  

9781475722635

ISBN 10:   147572263
Pages:   356
Publication Date:   14 December 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of 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.

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