出版社:世界图书出版公司北京公司
年代:2007
定价:69.0
本书是代数学基本观点的一个很好的展示。既是一本教科书,也是一本很好的参考书。作为一本很好的教科书,前几章较后几章讲述得较详细,也较慢;作为参考资料,也包含了不少本书用不到的基本概念,所以本书的材料也较一般书的材料稍微偏多。内容主要有:同调和基础群;覆盖空间和纤维化;多面体;谱序列和球面同调群。
Preface
Acknowledgments
CHAPTERⅠGeneralTopology
1.MetricSpaces
2.TopologicalSpaces
3.Subspaces
4.ConnectivityandComponents
5.SeparationAxioms
6.Nets(Moore-SmithConvergence)
7.Compactness
8.Products
9.MetricSpacesAgain
10.ExistenceofRealValuedFunctions
11.LocallyCompactSpaces
12.ParacompactSpaces
13.QuotientSpaces
14.Homotopy
15.TopologicalGroups
16.ConvexBodies
17.TheBaireCategoryTheorem
CHAPTERⅡDifferentiableManifolds
1.TheImplicitFunctionTheorem
2.DifferentiableManifolds
3.LocalCoordinates
4.InducedStructuresandExamples
5.TangentVectorsandDifferentials
6.SardsTheoremandRegularValues
7.LocalPropertiesofImmersionsandSubmersions
8.VectorFieldsandFlows
9.TangentBundles
10.EmbeddinginEuclideanSpace
11.TubularNeighborhoodsandApproximations
12.ClassicalLieGroups
13.FiberBundles
14.InducedBundlesandWhitneySums
15.Transversality
16.Thom-PontryaginTheory
CHAPTERⅢFundamentalGroup
1.HomotopyGroups
2.TheFundamentalGroup
3.CoveringSpaces
4.TheLiftingTheorem
5.TheActionofnlontheFiber
6.DeckTransformations
7.ProperlyDiscontinuousActions
8.ClassificationofCoveringSpaces
9.TheSeifert-VanKampenTheorem
10.RemarksonSO(3)
CHAPTERⅣHomologyTheory
1.HomologyGroups
2.TheZerothHomologyGroup
3.TheFirstHomologyGroup
4.FunctorialProperties
5.HomologicalAlgebra
6.AxiomsforHomology
7.ComputationofDegrees
8.CW-Complexes
9.ConventionsforCW-Complexes
10.CellularHomology
11.CellularMaps
12.ProductsofCW-Complexes
13.EulersFormula
14.HomologyofRealProjectiveSpace
15.SingularHomology
16.TheCrossProduct
17.Subdivision
18.TheMayer-VietorisSequence
19.TheGeneralizedJordanCurveTheorem
20.TheBorsuk-UlamTheorem
21.SimplicialComplexes
22.SimplicialMaps
23.TheLefschetz-HopfFixedPointTheorem
CHAPTERⅤCohomology
1.MultilinearAlgebra
2.DifferentialForms
3.IntegrationofForms
4.StokesTheorem
5.RelationshiptoSingularHomology
6.MoreHomologicatAlgebra
7.UniversalCoefficientTheorems
8.ExcisionandHomotopy
9.deRhamsTheorem
10.ThedeRhamTheoryofCPn
11.HopfsTheoremonMapstoSpheres
12.DifferentialFormsonCompactLieGroups
CHAPTERⅥProductsandDuality
1.TheCrossProductandtheKfinnethTheorem
2.ASignConvention
3.TheCohomologyCrossProduct
4.TheCupProduct
5.TheCapProduct
6.ClassicalOutlookonDuality
7.TheOrientationBundle
8.DualityTheorems
9.DualityonCompactManifoldswithBoundary
10.ApplicationsofDuality
11.IntersectionTheory
12.TheEulerClass,LefschetzNumbers,andVectorFields
13.TheGysinSequence
14.LefschetzCoincidenceTheory
15.SteenrodOperations
16.ConstructionoftheSteenrodSquares
17.Stiefel-WhitneyClasses
18.Plumbing
CHAPTERⅦIHomotopyTheory
1.Cofibrations
2.TheCompact-OpenTopology
3.H-Spaces,H-Groups,andH-Cogroups
4.HomotopyGroups
5.TheHomotopySequenceofaPair
6.FiberSpaces
7.FreeHomotopy
8.ClassicalGroupsandAssociatedManifolds
9.TheHomotopyAdditionTheorem
10.TheHurewiczTheorem
11.TheWhiteheadTheorem
12.Eilenberg-MacLaneSpaces
13.ObstructionTheory
14.ObstructionCochainsandVectorBundles
Appendices
App.A.TheAdditivityAxiom
App.B.BackgroundinSetTheory
App.C.CriticalValues
App.D.DirectLimits
App.E.EuclideanNeighborhoodRetracts
Bibliography
IndexofSymbols
Index
Sincethebeginningoftime,oratleasttheeraofArchimedes,smoothmanifolds(curves,surfaces,mechanicalconfigurations,theuniverse)havebeenacentralfocusinmathematics.Theyhavealwaysbeenatthecoreofinterestintopology.AftertheseminalworkofMilnor,Smale,andmanyothers,inthelasthalfofthiscentury,thetopologicalaspectsofsmoothmanifolds,asdistinctfromthedifferentialgeometricaspects,becameasubjectinitsownright.Whilethemajorportionofthisbookisdevotedtoalgebraictopology,Iattempttogivethereadersomeglimpsesintothebeautifulandimportantrealmofsmoothmanifoldsalongtheway,andtoinstillthetenetthatthealgebraictoolsareprimarilyintendedfortheunderstandingofthegeometricworld.
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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) | 69.0 | 语种 | 英文 |
尺寸 | 14 | 装帧 | 平装 |
页数 | 印数 | 1000 |
拓扑与几何是世界图书出版公司北京公司于2007.10出版的中图分类号为 O18 的主题关于 几何-英文 ,拓扑-英文 的书籍。
(美) 沙利文 (Sullivan,D.P.) , 著
汪容, 著
华东师范大学数学科学学院, 编著
华东师范大学数学科学学院, 编著
(德) I.M.辛格, (德) J.A.索普, 著
(俄罗斯) 米先柯, (俄罗斯) 福明柯, 著
古志鸣, 编著
(俄罗斯) 波斯特尼科夫 (Postnikov,M.M.) , 著
(俄罗斯) 加姆克列利泽 (Gamkrelidze R.V.) , 编著