algebraic topology 2000 hatcher

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1、AllenHatcherCopyrightc2000byAllenHatcherPaperorelectroniccopiesfornoncommercialusemaybemadefreelywithoutexplicitpermissionfromtheauthor.Allotherrightsreserved.TableofContentsChapter0.SomeUnderlyingGeometricNotions.....1HomotopyandHomotopyType1.CellComple

2、xes5.OperationsonSpaces8.TwoCriteriaforHomotopyEquivalence11.TheHomotopyExtensionProperty14.Chapter1.TheFundamentalGroup.............211.BasicConstructions.......................25PathsandHomotopy25.TheFundamentalGroupoftheCircle28.InducedHomomorphisms34

3、.2.VanKampen’sTheorem....................39FreeProductsofGroups39.ThevanKampenTheorem41.ApplicationstoCellComplexes49.3.CoveringSpaces.........................55LiftingProperties59.TheClassificationofCoveringSpaces62.DeckTransformationsandGroupActions69.A

4、dditionalTopicsA.GraphsandFreeGroups81.B.K(G,1)SpacesandGraphsofGroups86.Chapter2.Homology.......................971.SimplicialandSingularHomology..............102ÑComplexes102.SimplicialHomology104.SingularHomology108.HomotopyInvariance110.ExactSequence

5、sandExcision113.TheEquivalenceofSimplicialandSingularHomology128.2.ComputationsandApplications...............134Degree134.CellularHomology137.Mayer-VietorisSequences149.HomologywithCoefficients153.3.TheFormalViewpoint.....................160AxiomsforHomol

6、ogy160.CategoriesandFunctors162.AdditionalTopicsA.HomologyandFundamentalGroup166.B.ClassicalApplications168.C.SimplicialApproximation175.Chapter3.Cohomology.....................1831.CohomologyGroups......................188TheUniversalCoefficientTheorem18

7、8.CohomologyofSpaces195.2.CupProduct...........................204TheCohomologyRing209.AKunnethFormula215.¨SpaceswithPolynomialCohomology221.3.Poincar´eDuality.........................228OrientationsandHomology231.TheDualityTheorem237.ConnectionwithCupPr

8、oduct247.OtherFormsofDuality250.AdditionalTopicsA.TheUniversalCoefficientTheoremforHomology259.B.TheGeneralKunnethFormula266.¨C.H–SpacesandHopfAlgebras279.D.TheCohomologyofSO(n)291.E.BocksteinHomomorphisms301.F.Limits309.G.