纤维丛

(美) 休斯莫勒 (Husemoller,D.) , 著

出版社：世界图书出版公司北京公司

年代：2009

定价：38.0

书籍简介:

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。

书籍目录:

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

……

内容摘要:

　　Inthisedition,wehaveaddedtwonewchapters,Chapter7onthegaugegroupofaprincipalbundleandChapter19onthedefinitionofChernclassesbydifferentialforms.Thesesubjectshavetakenonspecialimportancewhenweconsidernewapplicationsofthefibrebundletheoryespeciallytomathematicalphysics.Forthesetwochapters,theauthorprofitedfromdiscussionswithProfessorM.S.Narasimhan.Theideaofusingthetermbundleforwhatisjustamap,butiseventuallyafibrebundleprojection,isduetoGrothendieck.

书籍规格:

书籍详细信息
书名	纤维丛站内查询相似图书
	9787510004452 如需购买下载《纤维丛》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN
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

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书籍信息归属:

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。