Algebraic_Topology

《Algebraic_Topology》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、AllenHatcherCopyrightc2001byAllenHatcherPaperorelectroniccopiesfornoncommercialusemaybemadefreelywithoutexplicitpermissionfromtheauthor.Allotherrightsreserved.Preface.................................ixStandardNotationsxii.Chapter0.SomeUnderlyingGeometricNot

2、ions.....1HomotopyandHomotopyType1.CellComplexes5.OperationsonSpaces8.TwoCriteriaforHomotopyEquivalence10.TheHomotopyExtensionProperty14.Chapter1.TheFundamentalGroup.............211.1.BasicConstructions.....................25PathsandHomotopy25.TheFundamenta

3、lGroupoftheCircle28.InducedHomomorphisms33.1.2.VanKampen’sTheorem...................38FreeProductsofGroups39.ThevanKampenTheorem41.ApplicationstoCellComplexes48.1.3.CoveringSpaces........................54LiftingProperties58.TheClassificationofCoveringSpaces

4、61.DeckTransformationsandGroupActions68.AdditionalTopics1.A.GraphsandFreeGroups81.1.B.K(G,1)SpacesandGraphsofGroups85.viTableofContentsChapter2.Homology.......................952.1.SimplicialandSingularHomology.............100ÑComplexes100.SimplicialHomolog

5、y102.SingularHomology106.HomotopyInvariance108.ExactSequencesandExcision111.TheEquivalenceofSimplicialandSingularHomology126.2.2.ComputationsandApplications..............132Degree132.CellularHomology135.Mayer-VietorisSequences147.HomologywithCoefficients151.

6、2.3.TheFormalViewpoint....................158AxiomsforHomology158.CategoriesandFunctors160.AdditionalTopics2.A.HomologyandFundamentalGroup164.2.B.ClassicalApplications167.2.C.SimplicialApproximation175.Chapter3.Cohomology.....................1833.1.Cohomolo

7、gyGroups.....................188TheUniversalCoefficientTheorem188.CohomologyofSpaces195.3.2.CupProduct..........................204TheCohomologyRing209.AKunnethFormula216.¨SpaceswithPolynomialCohomology222.3.3.Poincar´eDuality........................228Orien

8、tationsandHomology231.TheDualityTheorem237.ConnectionwithCupProduct247.OtherFormsofDuality250.AdditionalTopics3.A.UniversalCoefficientsforHomology259.3.B.TheGeneralKunnethFormula266.¨3.C.H–SpacesandHopf