Fibre bundles纤维捆
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作者： Dale Husemoller 著
出 版 社：
出版时间： 1993-12-1字数：版次： 1页数： 353印刷时间： 1993/12/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387940878包装： 精装内容简介
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.
目录
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
CHAPTER 1 Preliminaries on Homotopy Theory
1. Category Theory and Homotopy Theory
2. Complexes
3. The Spaces Map (X, Y) and Mapo (X, Y)
4. Homotopy Groups of Spaces
5. Fibre Maps
PART Ⅰ THE GENERAL THEORY OF FIBRE BUNDLES
CHAPTER 2 Generalities on Bundles
1. Definition of Bundles and Cross Sections
2. Examples of Bundles and Cross Sections
3. Morphisms of Bundles
4. Products and Fibre Products
5. Restrictions of Bundles and Induced Bundles
6. Local Properties of Bundles
7. Prolongation of Cross Sections
Exercises
CHAPTER 3 Vector Bundles
1. Definition and Examples of Vector Bundles
2. Morphisms of Vector Bundles
3. Induced Vector Bundles
4. Homotopy Properties of Vector Bundles
5. Construction of Gauss Maps
6. Homotopies of Gauss Maps
7. Functorial Description of the Homotopy Classification of Vector Bundles
8. Kernel, Image, and Cokernel of Morphisms with Constant Rank
9. Riemannian and Hermitian Metrics on Vector Bundles
Exercises
CHAPTER 4 General Fibre Bundles
1. Bundles Defined by Transformation Groups
2. Definition and Examples of Principal Bundles
3. Categories of Principal Bundles
4. Induced Bundles of Principal Bundles
5. Definition of Fibre Bundles
6. Functorial Properties of Fibre Bundles
7. Trivial and Locally Trivial Fibre Bundles
8. Description of Cross Sections of a Fibre Bundle
9. Numerable Principal Bundles over B x [0, 1]
10. The Cofunctor k
11. The Milnor Construction
12. Homotopy Classification of Numerable Principal G-Bundles
13. Homotopy Classification of Principal G-Bundles over
CW-Complexes
Exercises
CHAPTER 5 Local Coordinate Description of Fibre Bundles
1. Automorphisms of Trivial Fibre Bundles
2. Charts and Transition Functions
3. Construction of Bundles with Given Transition Functions
4. Transition Functions and Induced Bundles
5. Local Representation of Vector Bundle Morphisms
6. Operations on Vector Bundles
7. Transition Functions for Bundles with Metrics
Exercises
CHAPTER 6 Change of Structure Group in Fibre Bundles
1. Fibre Bundles with Homogeneous Spaces as Fibres
……
PART Ⅱ ELEMENTS OF K-THEORY
PART Ⅲ CHARACTERISTIC CLASSES
Appendix 1 Dold's Theory of Local Properties of Bundles
Appendix 2 On the Double Suspension
Bibliography
Index