代数拓扑学 algebraic topology_allen hatcher

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1、AllenHatcherCopyrightc2002byCambridgeUniversityPressSinglepaperorelectroniccopiesfornoncommercialpersonalusemaybemadewithoutexplicitpermissionfromtheauthororpublisher.Allotherrightsreserved.Preface..................................ixStandardNotationsxii.

2、Chapter0.SomeUnderlyingGeometricNotions.....1HomotopyandHomotopyType1.CellComplexes5.OperationsonSpaces8.TwoCriteriaforHomotopyEquivalence10.TheHomotopyExtensionProperty14.Chapter1.TheFundamentalGroup.............211.1.BasicConstructions.................

3、....25PathsandHomotopy25.TheFundamentalGroupoftheCircle29.InducedHomomorphisms34.1.2.VanKampen’sTheorem...................40FreeProductsofGroups41.ThevanKampenTheorem43.ApplicationstoCellComplexes50.1.3.CoveringSpaces........................56LiftingProp

4、erties60.TheClassificationofCoveringSpaces63.DeckTransformationsandGroupActions70.AdditionalTopics1.A.GraphsandFreeGroups83.1.B.K(G,1)SpacesandGraphsofGroups87.Chapter2.Homology.......................972.1.SimplicialandSingularHomology.............102ÑCom

5、plexes102.SimplicialHomology104.SingularHomology108.HomotopyInvariance110.ExactSequencesandExcision113.TheEquivalenceofSimplicialandSingularHomology128.2.2.ComputationsandApplications..............134Degree134.CellularHomology137.Mayer-VietorisSequences1

6、49.HomologywithCoefficients153.2.3.TheFormalViewpoint....................160AxiomsforHomology160.CategoriesandFunctors162.AdditionalTopics2.A.HomologyandFundamentalGroup166.2.B.ClassicalApplications169.2.C.SimplicialApproximation177.Chapter3.Cohomology...

7、..................1853.1.CohomologyGroups.....................190TheUniversalCoefficientTheorem190.CohomologyofSpaces197.3.2.CupProduct..........................206TheCohomologyRing211.AKunnethFormula218.¨SpaceswithPolynomialCohomology224.3.3.Poincar´eDua

8、lity........................230OrientationsandHomology233.TheDualityTheorem239.ConnectionwithCupProduct249.OtherFormsofDuality252.AdditionalTopics3.A.UniversalCoefficientsforHomology261.3.B.TheGeneralKunnethFormula268.¨3.C.