出版社：世界图书出版公司北京公司
年代：2009
定价：38.0
本书全面总结了50年代以来纤维丛理论的重大进展和成果，主要有以下三方面内容：（一）拓扑群构造成泛纤维丛；（二）K理论，证明了Hopf不变元的不存在性和球面向量场问题；（三）示性类及它们在流行上的应用，介绍了Grothendieck对Hirzebruch方法的重要改进。
PrefacetotheThirdEdition
PrefacetotheSecondEdition
PrefacetotheFirstEdition
CHAPTER1PreliminariesonHomotopyTheory
1.CategoryTheoryandHomotopyTheory
2.Complexes
3.TheSpacesMap(X,Y)andMap0(X,Y)
4.HomotopyGroupsofSpaces
5.FibreMaps
PARTITHEGENERALTHEORYOFFIBREBUNDLES
CHAPTER2GeneralitiesonBundles
1.DefinitionofBundlesandCrossSections
2.ExamplesofBundlesandCrossSections
3.MorphismsofBundles
4.ProductsandFibreProducts
5.RestrictionsofBundlesandInducedBundles
6.LocalPropertiesofBundles
7.ProlongationofCrossSections
Exercises
CHAPTER3VectorBundles
1.DefinitionandExamplesofVectorBundles
2.MorphismsofVectorBundles
3.inducedVectorBundles
4.HomotopyPropertiesofVectorBundles
5.ConstructionofGaussMaps
6.HomotopiesofGaussMaps
7.FunctorialDescriptionoftheHomotopyClassificationofVectorBundles
8.Kernel,Image,andCokernelofMorphismswithConstantRank
9.RiemannianandHermitianMetricsonVectorBundles
Exercises
CHAPTER4GeneralFibreBundles
1.BundlesDefinedbyTransformationGroups
2.DefinitionandExamplesofPrincipalBundles
3.CategoriesofPrincipalBundles
4.InducedBundlesofPrincipalBundles
5.DefinitionofFibreBundles
6.FunctorialPropertiesofFibreBundles
7.TrivialandLocallyTrivialFibreBundles
8.DescriptionofCrossSectionsofaFibreBundle
9.NumerablePrincipalBundlesoverBx[0,I]
10.TheCofunctork
11.TheMilnorConstruction
12.HomotopyClassificationofNumerablePrincipalG-Bundles
13.HomotopyClassificationofPrincipalG-BundlesoverCW-Complexes
Exercises
CHAPTER5LocalCoordinateDescriptionofFibreBundles
1.AutomorphismsofTrivialFibreBundles
2.ChartsandTransitionFunctions
3.ConstructionofBundleswithGivenTransitionFunctions
4.TransitionFunctionsandInducedBundles
5.LocalRepresentationofVectorBundleMorphisms
6.OperationsonVectorBundles
7.TransitionFunctionsforBundleswithMetricsExercises
CHAPTER6ChangeofStructureGroupinFibreBundles
1.FibreBundleswithHomogeneousSpacesasFibres
……
Inthisedition,wehaveaddedtwonewchapters,Chapter7onthegaugegroupofaprincipalbundleandChapter19onthedefinitionofChernclassesbydifferentialforms.Thesesubjectshavetakenonspecialimportancewhenweconsidernewapplicationsofthefibrebundletheoryespeciallytomathematicalphysics.Forthesetwochapters,theauthorprofitedfromdiscussionswithProfessorM.S.Narasimhan.Theideaofusingthetermbundleforwhatisjustamap,butiseventuallyafibrebundleprojection,isduetoGrothendieck.
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 38.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
纤维丛是世界图书出版公司北京公司于2009.04出版的中图分类号为 O189.3 的主题关于 纤维丛－英文 的书籍。