纤维丛（第3版）

图书标准信息

• 作者 [美]休斯莫勒 著
• 出版社 世界图书出版公司
• 出版时间 2009-04
• 版次 1
• ISBN 9787510004452
• 定价 38.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 352页
• 正文语种 英语

【内容简介】

Thenotionofafibrebundlefirstaroseoutofquestionsposedinthe1930sonthetopologyandgeometryofmanifolds.Bytheyear1950，thedefinitionoffibrebundlehadbeenclearlyformulated，thehomotopyclassificationoffibrebundlesachieved，andthetheoryofcharacteristicclassesoffibrebundlesdevelopedbyseveralmathematicians：Chern，Pontrjagin，Stiefel，andWhitney.Steenrodsbook，whichappearedin1950，gaveacoherenttreatmentofthesubjectuptothattime.
About1955，Miinorgaveaconstructionorauniversalfibrebundleforanytopologicalgroup.ThisconstructionisalsoincludedinPartIalongwithanelementaryproofthatthebundleisuniversal.

【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[0，1]
10.TheCofunctork
11.TheMilnorConstruction
12.HomotopyClassificationofNumerablePrincipalG-Bundles
13.HomotopyClassificationofPrincipalG-Bundlesover
CW-Complexes
Exercises

CHAPTER5LocalCoordinateDescriptionofFibreBundles
1.AutomorphismsofTrivialFibreBundles
2.ChartsandTransitionFunctions
3.ConstructionofBundleswithGivenTransitionFunctions
4.TransitionFunctionsandInducedBundles
5.LocalRepresentationofVectorBundleMorphisms
6.OperationsonVectorBundles
7.TransitionFunctionsforBundleswithMetricsExercises

CHAPTER6ChangeofStructureGroupinFibreBundles
1.FibreBundleswithHomogeneousSpacesasFibres2.ProlongationandRestrictionofPrincipalBund
les
3.RestrictionandProlongationofStructureGroupforFibreBundles
4.LocalCoordinateDescription.ofChangeofStructureGroup
5.ClassifyingSpacesandtheReductionofStructureGroupExercises

CHAPTER7TheGaugeGroupofaPrincipalBundle
1.DefinitionoftheGaugeGroup
2.TheUniversalStandardPrincipalBundleoftheGaugeGroup
3.TheStandardPrincipalBundleasaUniversalBundle
4.AbelianGaugeGroupsandtheKiinnethFormula

CHPTER8
CalculationsInvolvingtheClassicalGroups
1.StiefelVarietiesandtheClassicalGroups
2.GrassmannManifoldsandtheClassicalGroups
3.LocalTrivialityofProjectionsfromStiefelVarieties
4.StabilityoftheHomotopyGroupsoftheClassicalGroups
5.VanishingofLowerHomotopyGroupsofStiefelVarieties
6.UniversalBundlesandClassifyingSpacesfortheClassicalGroups
7.UniversalVectorBundles
8.DescriptionofallLocallyTrivialFibreBundlesoverSuspensions
9.CharacteristicMapoftheTangentBundleoverSn
10.HomotopyPropertiesofCharacteristicMaps
11.HomotopyGroupsofStiefelVarieties
12.SomeoftheHomotopyGroupsoftheClassicalGroups
Exercises
PARTII
ELEMENTSOFK-THEORY

CHAPTER9
StabilityPropertiesofVectorBundles
1.TrivialSummandsofVectorBundles
2.HomotopyClassificationandWhitneySums
3.TheKCofunctors
4.CorepresentationsofKF
5.HomotopyGroupsofClassicalGroupsandKF(Si)
Exercises

CHAPTER10
RelativeK-Theory
1.CollapsingofTrivializedBundles
2.ExactSequencesinRelativeK-Theory
3.ProductsinK-Theory
4.TheCofunctorL(X，A)
5.TheDifferenceMorphism
6.ProductsinL(X，A)
7.TheClutchingConstruction
8.TheCofunctorLn(X.A)
9.Half-ExactCofunctors
Exercises

CHAPTER11
BottPeriodicityintheComplexCase
1.K-TheoryInterpretationofthePeriodicityResult
2.ComplexVectorBundlesoverXxS2
3.AnalysisofPolynomialClutchingMaps
4.AnalysisofLinearClutchingMaps
5.TheInversetothePeriodicityIsomorphism

CHAPTER12
CliffordAlgebras
1.UnitTangentVectorFieldsonSpheres：I
2.OrthogonalMultiplications
3.GeneralitiesonQuadraticForms
4.CliffordAlgebraofaQuadraticForm
5.CalculationsofCliffordAlgebras
6，CliffordModules
7.TensorProductsofCliffordModules
8.UnitTangentVectorFieldsonSpheres：II
9.TheGroupSpin(k)
Exercises

CHAPTER13
TheAdamsOperationsandRepresentations
1.λ-Rings
2.TheAdamsψ-Operationsinλ-Ring
3.TheγiOperations
4.GeneralitiesonG-Modules
5.TheRepresentationRingofaGroupGandVectorBundles
6.SemisimplicityofG-ModulesoverCompactGroups
7.CharactersandtheStructureoftheGroupRF(G)
8.MaximalTort
9.TheRepresentationRingofaTorus
10.TheO-OperationsonK(X)andKO(X)
11.TheO-OperationsonK(Sn)

CHAPTER14
RepresentationRingsofClassicalGroups
1.SymmetricFunctions
2.MaximalToriinSU(n)andU(n)
3.TheRepresentationRingsofSU(n)andU(n)
4.MaximalToffinSp(n)
5.FormalIdentitiesinPolynomialRings
6.TheRepresentationRingofSp(n)
7.MaximalToriandtheWeylGroupofSO(n)
8.MaximalToriandtheWeylGroupofSpin(n)
9.SpecialRepresentationsofSO(n)andSpin(n)
10.CalculationofRSO(n)andRSpin(n)
11.RelationBetweenRealandComplexRepresentationRings
12.ExamplesofRealandQuaternionicRepresentations
13.SpinorRepresentationsandtheK-GroupsofSpheres

CHAPTER15
TheHopflnyariant
1.K-TheoryDefinitionoftheHopfInvariant
2.AlgebraicPropertiesoftheHopfInvariant
3.HopfInvariantandBidegree
4.NonexistenceofElementsofHopfInvariant1

CHAPTER16
VectorFieldsontheSphere
1.ThornSpacesofVectorBundles
2.S-Category
3.S-DualityandtheAtiyahDualityTheorem
4.FibreHomotopyType
5.StableFibreHomotopyEquivalence
6.TheGroupsJ(Sk)andKTop(Sk)
7.ThomSpacesandFibreHomotopyType
8.S-DualityandS-Reducibility
9.NonexistenceofVectorFieldsandReducibility
10.NonexistenceofVectorFieldsandCoreducibility
11.NonexistenceofVectorFieldsandJ(RPk)
12.RealK-GroupsofRealProjectiveSpaces
13.RelationBetweenKO(RPn)andJ(RPn)
14.RemarksontheAdamsConjecture
PARTIII
CHARACTERISTICCLASSES

CHAPTER17
ChernClassesandStiefeI-WhitneyClasses
1.TheLeray-HirschTheorem
2.DefinitionoftheStiefei-WhitneyClassesandChernClasses
3.AxiomaticPropertiesoftheCharacteristicClasses
4.StabilityPropertiesandExamplesofCharacteristicClasses
5.SplittingMapsandUniquenessofCharacteristicClasses
6.ExistenceoftheCharacteristicClasses
7.FundamentalClassofSphereBundles.GysinSequence
8.MultiplicativePropertyoftheEulerClass
9.DefinitionofStiefeI-WhitneyClassesUsingtheSquaring
OperationsofSteenrod
10.TheThomIsomorphism
11.RelationsBetweenRealandComplexVectorBundles
12.OrientabilityandStiefeI-WhitneyClasses
Exercises

CHAPTER18
DifferentiableManifolds
1.GeneralitiesonManifolds
2.TheTangentBundletoaManifold
3.OrientationinEuclideanSpaces
4.OrientationofManifolds
5.DualityinManifolds
6.ThornClassoftheTangentBundle
7.EulerCharacteristicandClassofaManifold
8.WusFormulafortheStiefeI-WhitneyClassofaManifold
9.StiefeI-WhitneyNumbersandCobordism
10.ImmersionsandEmbeddingsofManifolds
Exercises

CHAPTER19
CharacteristicClassesandConnections
1.DifferentialFormsanddeRhamCohomology
2.ConnectionsonaVectorBundle
3.InvariantPolynomialsintheCurvatureofaConnection
4.HomotopyPropertiesofConnectionsandCurvature
5.HomotopytotheTrivialConnectionandtheChern-SimonsForm
6.TheLevi-CivitaorRiemannianConnection

CHAPTER20
GeneralTheoryofCharacteristicClasses
1.TheYonedaRepresentationTheorem
2.GeneralitiesonCharacteristicClasses
3.ComplexCharacteristicClassesinDimensionn
4.ComplexCharacteristicClasses
5.RealCharacteristicClassesMod2
6.2-DivisibleRealCharacteristicClassesinDimensionn
7.OrientedEven-DimensionalRealCharacteristicClasses
8.ExamplesandApplications
9.BottPeriodicityandIntegralityTheorems
10.ComparisonofK-TheoryandCohomologyDefinitions
ofHopfInvariant
11.TheBorel-HirzebruchDescriptionofCharacteristicClasses

Appendix1
DoldsTheoryofLocalPropertiesofBundles

Appendix2
OntheDoubleSuspension
1.H*(ΩS(X))asanAlgebraicFunctorofH(X)
2.ConnectivityofthePair(Ω2S2n+1，S2n-1)Localizedatp
3.DecompositionofSuspensionsofProductsandliS(X)
4.SingleSuspensionSequences
5.ModpHopfInvariant
6.SpacesWherethepthPowerIsZero
7.DoubleSuspensionSequences
8.StudyoftheBoundaryMap△：Ω3S2np+1→ΩS2n-1
Bibliography
Index