代数拓扑讲义

图书标准信息

• 作者 [德]多德 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510004995
• 定价 65.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 377页
• 正文语种 英语

【内容简介】

Thisisessentiallyabookonsingularhomologyandcohomologywithspecialemphasisonproductsandmanifolds.Itdoesnottreathomotopytheoryexceptforsomebasicnotions，someexamples，andsomeapplica-tionsofhomologytohomotopy.Nordoesitdealwithgeneral（ised）homology，butmanyformulationsandargumentsonsingularhomologyaresochosenthattheyalsoapplytogeneralhomology.BecauseoftheseabsencesIhavealsoomittedspectralsequences，theirmainapplicationsintopologybeingtohomotopyandgeneralhomologytheory.ech-cohomologyistreatedinasimpleadhocfashionforlocallycompactsubsetsofmanifolds;ashortsystematictreatmentforarbitraryspaces，emphasizingtheuniversalpropertyofthe（ech-procedure，iscontainedinanappendix.Thebookgrewoutofaone-yearscourseonalgebraictopology，anditcanserveasatextforsuchacourse.Forashorterbasiccourse，sayofhalfayear，onemightusechaptersⅡⅢⅣ（§1-4），Ⅴ（§I-5，7，8），Ⅵ（§3，7，9，11，12）.Asprerequisitesthestudentshouldknowtheelementarypartsofgeneraltopology，abeliangrouptheory，andthelanguageofcategories-althoughourchapterⅠprovidesalittlehelpwiththelattertwo.Forpedagogicalreasons，IhavetreatedintegralhomologyonlyuptochapterⅥifareaderorteacherpreferstohavegeneralcoefficientsfromthebeginningheneedstomakeonlyminoradaptions.Astotheoutlayofthebook，thereareeightchapters，Ⅰ-Ⅷandnappendix，A;eachoftheseissubdividedintoseveral

【目录】

ChapterⅠPreliminariesonCategories，AbelianGroups，andHomotopy
§1CategoriesandFunctors
§2AbelianGroups(Exactness，DirectSums，FreeAbelianGroups)
§3Homotopy

ChapterⅡHomologyofComplexes
§1Complexes
§2ConnectingHomomorphism，ExactHomologySequence
§3Chain-Homotopy
§4FreeComplexes

ChapterⅢSingularHomology
§1StandardSimplicesandTheirLinearMaps
§2TheSingularComplex
§3SingularHomology
§4SpecialCases
§5InvarianceunderHomotopy
§6BarycentricSubdivision
§7SmallSimplices.Excision
§8Mayer-VietorisSequences

ChapterⅣApplicationstoEuclideanSpace
§1StandardMapsbetweenCellsandSpheres
§2HomologyofCellsandSpheres
§3LocalHomology
§4TheDegreeofaMap
§5LocalDegrees
§6HomologyPropertiesofNeighborhoodRetractsinIRn
§7JordanTheorem，InvarianceofDomain
§8EuclideanNeighborhoodRetracts(ENRs)

ChapterⅤCellularDecompositionandCellularHomology
§1CellularSpaces
§2CW-Spaces
§3Examples
§4HomologyPropertiesofCW-Spaces
§5TheEuler-PoincareCharacteristic
§6DescriptionofCellularChainMapsandoftheCellularBoundaryHomomorphism
§7SimplicialSpaces
§8SimplicialHomology

ChapterⅥFunctorsofComplexes
§1Modules
§2AdditiveFunctors
§3DerivedFunctors
§4UniversalCoefficientFormula
§5TensorandTorsionProducts
§6HomandExt
§7SingularHomologyandCohomologywithGeneralCoefficientGroups
§8TensorproductandBilinearity
§9TensorproductofComplexesKunnethFormula
§10HornofComplexes.HomotopyClassificationofChainMaps
§11AcyclicModels
§12TheEilenberg-ZilberTheorem.KunnethFormulasforSpaces

ChapterⅦProducts
§1TheScalarProduct
§2TheExteriorHomologyProduct
§3TheInteriorHomologyProduct(PontrjaginProduct
§4IntersectionNumbersinIRn
§5TheFixedPointIndex
§6TheLefschetz-HopfFixedPointTheorem
§7TheExteriorCohomologyProduct
§8TheInteriorCohomologyProductProduct
§9．ProductsinProjectiveSpaces．HopfMapsandHopfInvariant
§10HopfAlgebras
§llTheCohomologySlantProduct
§12TheCap-Product(Product)
§13TheHomologySlantProduct，andthePontrjaginSlantProductManffolds

ChapterⅧManifolds
§lElementaryPropertiesofManifolds
§2TheOrientationBundleofaManifold
§3HomologyofDimension≧ninn．Manifolds
§4FundamentalClassandDegree
§5Limits
§6CechCohomologyofLocallyCompactSubsetsof
§7Poincar6-LefschetzDuality
§8Examples，Applications
§9Dualityina-Manifolds
§10Transfer
§11ThomClass，ThornIsomorphism
§12TheGysinSequence．Examples
§13IntersectionofHomologyClassesKan．andCech-ExtensionsofFunctors

Appendix
§lLimitsofFunctors
§2PolyhcdtonsunderaSpace，andPartitionsofUnity
§3ExtendingFunctorsfromPolyhedronstomoreGeneralSpacesBibliographySubjectIndex

Bibliography
SubjectIndex