代数拓扑基础教程（英文版）

图书标准信息

• 作者 [美]曼斯 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510004803
• 定价 50.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 428页
• 正文语种 英语

【内容简介】

Thisbookisintendedtoserveasatextbookforacourseinalgebraictopologyatthebeginninggraduatelevel.Themaintopicscoveredaretheclassificationofcompact2-manifolds，thefundamentalgroup，coveringspaces，singularhomologytheory，andsingularcohomologytheory(includingcupproductsandthedualitytheoremsofPoincareandAlexander).ItconsistsofmaterialfromthefirstfivechaptersoftheauthorsearlierbookAlgebraicTopology：AnIntroduction(GTM56)togetherwithalmostallofhisbookSingularHomologyTheory(GTM70).Thismaterialfromthetwoearlierbookshasbeenrevised，corrected，andbroughtuptodate.Thereisenoughhereforafull-yearcourse.
Theauthorhastriedtogiveastraightforwardtreatmentofthesubjectmatter，strippedofallunnecessarydefinitions，terminology，andtechnicalmachinery.Hehasalsotried，whereverfeasible，toemphasizethegeometricmotivationbehindthevariousconcepts.Severalapplicationsofthemethodsofalgebraictopologytoconcretegeometrical-topologicalproblemsaregiven(e.g.，Brouwerfixedpointtheorem，Brouwer-Jordanseparationtheorem，lnvarianceofDomain.Borsuk-UlamtheoremS.

【目录】

Preface
NotationandTerminology
CHAPTERⅠ
Two-DimensionalManifolds
1.Introduction
2.DefinitionandExamplesofn-Manifolds
3.Orientablevs.NonorientableManifolds
4.ExamplesofCompact，Connected2-Manifolds
5.StatementoftheClassificationTheoremforCompactSurfaces
6.TriangulationsofCompactSurfaces
7.ProofofTheorem5.1
8.TheEulerCharacteristicofaSurface
References

CHAPTERⅡTheFundamentalGroup
1.Introduction
2.BasicNotationandTerminology
3.DefinitionoftheFundamentalGroupofaSpace
4.TheEffectofaContinuousMappingontheFundamentalGroup
5.TheFundamentalGroupofaCircleISInfiniteCyclic
6.Application：TheBrouwerFixed-PointTheoreminDimension2
7.TheFundamentalGroupofaProductSpace
8.HomotopyTypeandHomotopyEquivalenceofSpaces
References

CHAPTERⅢFreeGroupsandFreeProductsofGroups
1.Introduction
2.TheWeakProductofAbelianGroups
3.FreeAbelianGroups
4.FreeProductsofGroups
5.FreeGroups
6.ThePresentationofGroupsbyGeneratorsandRelations
7.UniversalMappingProblems
References

CHAPTERⅣSeifertandVanKampenTheoremontheFundamentalGroupoftheUnionofTwoSpaces.Applications
1.Introduction
2.StatementandProofoftheTheoremofSeifertandVanKampen
3.FirstApplicationofTheorem2.1
4.SecondApplicationofTheorem2.1
5.StructureoftheFundamentalGroupofaCompactSurface
6.ApplicationtoKnotTheory
7.ProofofLemma2.4
References

CHAPTERⅤCoveringSpaces
1.Introduction
2.DefinitionandSomeExamplesofCoveringSpaces
3.LiftingofPathstoaCoveringSpace
4.TheFundamentalGroupofaCoveringSpace
5.LiftingofArbitraryMapstoaCoveringSpace
6.HomomorphismsandAutomorphismsofCoveringSpaces
10.TheExistenceTheoremforCoveringSpacesReferences

CHAPTERⅥ
BackgroundandMotivationforHomologyTheory
1.Introduction
2.SummaryofSomeoftheBasicPropertiesofHomologyTheory
3.SomeExamplesofProblemswhichMotivatedtheDevelopmentofHomologyTheoryintheNineteenthCenturyReferences

CHAPTERⅦ
DefinitionsandBasicPropertiesofHomologyTheory
1.Introduction
2.DefinitionofCubicalSingularHomologyGroups
3.TheHomomorphismInducedbyaContinuousMap
4.TheHomotopyPropertyoftheInducedHomomorphisms
5.TheExactHomologySequenceofaPair
6.TheMainPropertiesofRelativeHomologyGroups
7.TheSubdivisionofSingularCubesandtheProofofTheorem6.4

CHAPTERⅧ
DeterminationoftheHomologyGroupsofCertainSpaces：
ApplicationsandFurtherPropertiesofHomologyTheory
1.Introduction
2.HomologyGroupsofCellsandSpheres——Applications
3.HomologyofFiniteGraphs
4.HomologyofCompactSurfaces
5.TheMayer-VietorisExactSequence
6.TheJordan-BrouwerSeparationTheoremandlnvarianceofDomain
7.TheRelationbetweentheFundamentalGroupandtheFirstHomologyGroup
References

CHAPTERⅨ
HomologyofCW-Complexes
1.Introduction
2.AdjoiningCellstoaSpace
3.CW-Complexes
4.TheHomologyGroupsofaCW-Complex
5.IncidenceNumbersandOrientationsofCells
6.RegularCW-Complexes
7.DeterminationofIncidenceNumbersforaRegularCellComplex
8.HomologyGroupsofaPseudomanifoldReferences

CHAPTERⅩ
HomologywithArbitraryCoefficientGroups
1.Introduction
2.ChainComplexes
3.DefinitionandBasicPropertiesofHomologywithArbitraryCoefficients
4.IntuitiveGeometricPictureofaCyclewithCoefficientsinG
5.CoefficientHomomorphismsandCoefficientExactSequences
6.TheUniversalCoefficientTheorem
7.FurtherPropertiesofHomologywithArbitraryCoefficientsReferences

CHAPTERⅪ
TheHomologyofProductSpaces
1.Introduction
2.TheProductofCW-ComplexesandtheTensorProductofChainComplexes
3.TheSingularChainComplexofaProductSpace
4.TheHomologyoftheTensorProductofChainComplexes(TheKiinnethTheorem)
5.ProofoftheEilenberg-ZilberTheorem
6.FormulasfortheHomologyGroupsofProductSpacesReferences