Hatcher， Algebraic Topology.PDF

《Hatcher， Algebraic Topology.PDF》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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

2、tricNotions.....1HomotopyandHomotopyType1.CellComplexes5.OperationsonSpaces8.TwoCriteriaforHomotopyEquivalence10.TheHomotopyExtensionProperty14.Chapter1.TheFundamentalGroup.............211.1.BasicConstructions.....................25PathsandHomotopy25.TheFundamentalGroupoftheCircle2

3、9.InducedHomomorphisms34.1.2.VanKampen’sTheorem...................40FreeProductsofGroups41.ThevanKampenTheorem43.ApplicationstoCellComplexes50.1.3.CoveringSpaces........................56LiftingProperties60.TheClassificationofCoveringSpaces63.DeckTransformationsandGroupActions70.Add

4、itionalTopics1.A.GraphsandFreeGroups83.1.B.K(G,1)SpacesandGraphsofGroups87.Chapter2.Homology.......................972.1.SimplicialandSingularHomology.............102ÑComplexes102.SimplicialHomology104.SingularHomology108.HomotopyInvariance110.ExactSequencesandExcision113.TheEquiva

5、lenceofSimplicialandSingularHomology128.2.2.ComputationsandApplications..............134Degree134.CellularHomology137.Mayer-VietorisSequences149.HomologywithCoefficients153.2.3.TheFormalViewpoint....................160AxiomsforHomology160.CategoriesandFunctors162.AdditionalTopics2.A

6、.HomologyandFundamentalGroup166.2.B.ClassicalApplications169.2.C.SimplicialApproximation177.Chapter3.Cohomology.....................1853.1.CohomologyGroups.....................190TheUniversalCoefficientTheorem190.CohomologyofSpaces197.3.2.CupProduct..........................206TheCo

7、homologyRing211.AKunnethFormula218.¨SpaceswithPolynomialCohomology224.3.3.Poincar´eDuality........................230OrientationsandHomology233.TheDualityTheorem239.ConnectionwithCupProduct249.OtherFormsofDuality252.AdditionalTopics3.A.UniversalCoefficientsforHomology261.3.B.TheGene

8、ralKunnethFormula268.¨3.C.