代数拓扑

图书标准信息

• 作者 W.Fulton 著
• 出版社 世界图书出版公司
• 出版时间 1997-09
• 版次 1
• ISBN 9787506233125
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 430页

【内容简介】

　　TotheTeacher.Thisbookisdesignedtointroduceastudenttosomeoftheimportantideasofalgebraictopologybyemphasizingtherelationsoftheseideaswithotherareasofmathematics.Ratherthanchoosingonepointofviewofmodemtopology(homotopytheory，simplicialcomplexes，singulartheory，axiomatichomology，differentialtopology，etc.)，weconcentrateourattentiononconcreteproblemsinlowdimensions，introducingonlyasmuchalgebraicmachineryasnecessaryfortheproblemswemeet.Thismakesitpossibletoseea.widervarietyofimportantfeaturesofthesubjectthanisusualinabeginningtext.Thebookisdesignedforstudentsofmathematicsorsciencewhoarenotaimingtobecomepracticingalgebraictopologists--without，wehope，discouragingbuddingtopologists.Wealsofeelthatthisapproachisinbetterharmonywiththehistoricaldevelopmentofthesubject.
　　本书为英文版。

【目录】

Preface
PARTI
CALCULUSINTHEPLANE
CHAPTER1PathIntegrals
1a.DifferentialFormsandPathIntegrals
1b.WhenArePathIntegralsIndependentofPath
1c.ACriterionforExactness
CHAPTER2AnglesandDeformations
2a.AngleFunctionsandWindingNumbers
2b.ReparametrizingandDeformingPaths
2e.VectorFieldsandFluidFlow
PARTIIWINDINGNUMBERS
CHAPTER3TheWindingNumber
3a.DefinitionoftheWindingNumber
3b.HomotopyandReparametrization
3c.VaryingthePoint
3d.DegreesandLocalDegrees
CHAPTER4ApplicationsofWindingNumbers
4a.TheFundamentalTheoremofAlgebra
4b.FixedPointsandRetractions
4c.Antipodes
4d.Sandwiches
PARTIIICOHOMOLOGYANDHOMOLOGY,I
CHAPTER5DeRhamCohomologyandtheJordanCurveTheorem
5a.DefinitionsoftheDeRhamGroups
5b.TheCoboundaryMap
5c.TheJordanCurveTheorem
5d.ApplicationsandVariations
CHAPTER6Homology
6a.Chains,Cycles,andHoU
6b.Boundaries,H1U,andWindingNumbers
6c.ChainsonGrids
6d.MapsandHomology
6e.TheFirstHomologyGroupforGeneralSpaces
PARTIVVECTORFIELDS
CHAPTER7IndicesofVectorFields
7a.VectorFieldsinthePlane
7b.ChangingCoordinates
7c.VectorFieldsonaSphere
CHAPTER8VectorFieldsonSurfaces
8a.VectorFieldsonaTorusandOtherSurfaces
8b.TheEulerCharacteristic
PARTVCOHOMOLOGYANDHOMOLOGY,II
CHAPTER9HolesandIntegrals
9a.MultiplyConnectedRegions
9b.IntegrationoverContinuousPathsandChains
9c.PeriodsofIntegrals
9d.ComplexIntegration
CHAPTER10Mayer-Vietoris
10a.TheBoundaryMap
10b.Mayer-VietorisforHomology
10c.VariationsandApplications
10d.Mayer-VietorisforCohomology
PARTVICOVERINGSPACESANDFUNDAMENTALGROUPS,I
CHAPTER11CovetingSpaces
CHAPTER12TheFundamentalGroup
PARTVIICOVERINGSPACESANDFUNDAMENTALGROUPS,II
CHAPTER13TheFundamentalGroupandCoveringSpaces
CHAPTER14TheVanKampenTheorem
PARTVIIICOHOMOLOGYANDHOMOLOGY,III
CHAPTER15Cohomology
CHAPTER16Variations
PARTIXTOPOLOGYOFSURFACES
CHAPTER17TheTopologyofSurfaces
CHAPTER18CohomologyonSurfaces
PARTXRIEMANNSURFACES
CHAPTER19RiemannSurfaces
CHAPTER20RiemannSurfacesandAlgebraicCurves
CHAPTER21TheRiemann-RochTheorem
PARTXIHIGHERDIMENSIONS
CHAPTER22TowardHigherDimensions
CHAPTER23HigherHomology
CHAPTER24Duality
APPENDICES
APPENDIXA
APPENDIXB
APPENDIXC
APPENDIXD
APPENDIXE
Indexofsymbols
Index