拓扑与几何

拓扑与几何

(美) 布里登 (Bredon,G.E.) , 著

出版社:世界图书出版公司北京公司

年代:2007

定价:69.0

书籍简介:

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。

书籍目录:

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

内容摘要:

  Sincethebeginningoftime,oratleasttheeraofArchimedes,smoothmanifolds(curves,surfaces,mechanicalconfigurations,theuniverse)havebeenacentralfocusinmathematics.Theyhavealwaysbeenatthecoreofinterestintopology.AftertheseminalworkofMilnor,Smale,andmanyothers,inthelasthalfofthiscentury,thetopologicalaspectsofsmoothmanifolds,asdistinctfromthedifferentialgeometricaspects,becameasubjectinitsownright.Whilethemajorportionofthisbookisdevotedtoalgebraictopology,Iattempttogivethereadersomeglimpsesintothebeautifulandimportantrealmofsmoothmanifoldsalongtheway,andtoinstillthetenetthatthealgebraictoolsareprimarilyintendedfortheunderstandingofthegeometricworld.

书籍规格:

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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

书籍信息归属:

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。