algebraic topology by hatcher 2002

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1、AllenHatcherCopyrightc2002byCambridgeUniversityPressSinglepaperorelectroniccopiesfornoncommercialpersonalusemaybemadewithoutexplicitpermissionfromtheauthororpublisher.Allotherrightsreserved.Preface..................................ixStandardNotationsxii.Chapter0.SomeUnderlyingGeometricNotions.

2、....1HomotopyandHomotopyType1.CellComplexes5.OperationsonSpaces8.TwoCriteriaforHomotopyEquivalence10.TheHomotopyExtensionProperty14.Chapter1.TheFundamentalGroup.............211.1.BasicConstructions.....................25PathsandHomotopy25.TheFundamentalGroupoftheCircle29.InducedHomomorphisms34

3、.1.2.VanKampen’sTheorem...................40FreeProductsofGroups41.ThevanKampenTheorem43.ApplicationstoCellComplexes50.1.3.CoveringSpaces........................56LiftingProperties60.TheClassificationofCoveringSpaces63.DeckTransformationsandGroupActions70.AdditionalTopics1.A.GraphsandFreeGroups

4、83.1.B.K(G,1)SpacesandGraphsofGroups87.Chapter2.Homology.......................972.1.SimplicialandSingularHomology.............102ÑComplexes102.SimplicialHomology104.SingularHomology108.HomotopyInvariance110.ExactSequencesandExcision113.TheEquivalenceofSimplicialandSingularHomology128.2.2.Comp

5、utationsandApplications..............134Degree134.CellularHomology137.Mayer-VietorisSequences149.HomologywithCoefficients153.2.3.TheFormalViewpoint....................160AxiomsforHomology160.CategoriesandFunctors162.AdditionalTopics2.A.HomologyandFundamentalGroup166.2.B.ClassicalApplications169

6、.2.C.SimplicialApproximation177.Chapter3.Cohomology.....................1853.1.CohomologyGroups.....................190TheUniversalCoefficientTheorem190.CohomologyofSpaces197.3.2.CupProduct..........................206TheCohomologyRing211.AKunnethFormula218.¨SpaceswithPolynomialCohomology224.3.

7、3.Poincar´eDuality........................230OrientationsandHomology233.TheDualityTheorem239.ConnectionwithCupProduct249.OtherFormsofDuality252.AdditionalTopics3.A.UniversalCoefficientsforHomology261.3.B.TheGeneralKunnethFormula268.¨3.C.