(ebook-pdf) Mathematics - Algebraic Topology

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1、AllenHatcherCopyrightc2000byAllenHatcherPaperorelectroniccopiesfornoncommercialusemaybemadefreelywithoutexplicitpermissionfromtheauthor.Allotherrightsreserved.TableofContentsChapter0.SomeUnderlyingGeometricNotions.....1HomotopyandHomotopyType1.CellComplexes5.

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

3、en’sTheorem....................39FreeProductsofGroups39.ThevanKampenTheorem41.ApplicationstoCellComplexes49.3.CoveringSpaces.........................55LiftingProperties59.TheClassificationofCoveringSpaces62.DeckTransformationsandGroupActions69.AdditionalTopics

4、A.GraphsandFreeGroups81.B.K(G,1)SpacesandGraphsofGroups86.Chapter2.Homology.......................971.SimplicialandSingularHomology..............102ÑComplexes102.SimplicialHomology104.SingularHomology108.HomotopyInvariance110.ExactSequencesandExcision113.TheE

5、quivalenceofSimplicialandSingularHomology128.2.ComputationsandApplications...............134Degree134.CellularHomology137.Mayer-VietorisSequences149.HomologywithCoefficients153.3.TheFormalViewpoint.....................160AxiomsforHomology160.CategoriesandFunct

6、ors162.AdditionalTopicsA.HomologyandFundamentalGroup166.B.ClassicalApplications168.C.SimplicialApproximation175.Chapter3.Cohomology.....................1831.CohomologyGroups......................188TheUniversalCoefficientTheorem188.CohomologyofSpaces195.2.CupP

7、roduct...........................204TheCohomologyRing209.AKunnethFormula215.¨SpaceswithPolynomialCohomology221.3.Poincar´eDuality.........................228OrientationsandHomology231.TheDualityTheorem237.ConnectionwithCupProduct247.OtherFormsofDuality250.Add

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