纤维丛
2009-4
世界图书出版公司
休斯莫勒
352
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In this edition，we have added two new chapters，Chapter 7 on the gauge group of a principal bundle and Chapter l 9 on the definition of Chern classes by djfrerential forms.These SUbjects have taken on special importance when we consider new applications of the fibre bundle theory especially to mathe- matical physics.For these two chapters.the author profited from discussions with Professor M.S.Narasimhan. The idea of using the term bundle for what iS iust a map，but iS eventually a fibre bundle projection，iS due to Grothendieck. The bibliography has been enlarged and updated.For example，in the Seifert reference rl 932]we find one of the first explicit references to the concept of fibrings. The first edition of the Fibre Bundies was translated into Russian under the title“PaccJIOeHHble pocTpaHcrna”in l 970 bv B.A.CKOBCKHX with gcneral editor M.M.OCTHHKOBa.The remarks and additions of the editor have been very USeful in this edition of the book.Thc author is very grateful to A.Voronov.who helped with translations of the additions from the RUS. sian text. Part of this revision was made while the author was a guest of the Max Planck lnstitut from 1988 to 89，the ETH during the summers of 1990 and 199l，the University 0f Heidelberg during the summer 0f 1992，and the Tata Institute for Fundamental Research during January 1990，1991.and 1992.It iS a pleasure tO acknowledge all these institutions as well as the Haverford College Faculty Research Fund.
The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950， the definition of fibre bundle had been clearly formulated， the homotopy classification of fibre bundles achieved， and the theory of characteristic classes of fibre bundles developed by several mathematicians： Chern， Pontrjagin， Stiefel， and Whitney. Steenrods book， which appeared in 1950， gavea coherent treatment of the subject up to that time. About 1955， Miinor gave a construction ora universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal.
Preface to the Third EditionPreface to the Second EditionPreface to the First EditionCHAPTER 1 Preliminaries on Homotopy Theory 1. Category Theory and Homotopy Theory 2. Complexes 3. The Spaces Map (X,'Y) and Map0 (X, Y) 4. Homotopy Groups of Spaces 5. Fibre MapsPART 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, I] 10. The Cofunctor k 11. The Milnor Construction 12. Homotopy Classification of Numerable Principal G-Bundles 13. Homotopy Classification of Principal G-Bundles over C W-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……
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比较满意，质量挺好
是新出的书，但本身书是很老的书，修改了几个版本。
纤维丛好
就是印刷质量欠缺，很多符号看不清