出版社：世界图书出版公司北京公司
年代：2007
定价：59.0
这本书是代数学基本观点的一个很好的展示。作者写本书的想法来源于1955年他在芝加哥大学的演讲。从那时候到现在代数学经历了很大的发展，这本书的思想的也是一直在更新，现在的这个版本是原版的修订版，可以称得上是一本真正的现代代数拓扑学。目次：引论；同调和基础群；覆盖空间和纤维化；多面体；同调；乘积；一般上同调理论和对偶性；同调论；障碍理论；谱序列和球面同调群。
INTRODUCTION
1Settheory
2Generaltopology
3Grouptheory
4Modules
5Euclideanspaces
1ROMOTOPYANDTHEFUNDAMENTALGROUP
1Categories
2Functors
3Homotopy
4Retractionanddeformation
5Hspaces
6Suspension
7Thefundamentalgroupoid
8Thefundamentalgroup
Exercises
2COVERINGSPACESANDFIBRATIONS
1Coveringprofections
2Thehomotopyliftingproperty
3Relationswiththefundamentalgroup
4Theliftingproblem
5Theclassificationofcoveringprojections
6Coveringtransformations
7Fiberbundles
8Fibrations
Exercises
3POLYHEDRA
1Simplicialcomplexes
2Linearityinsimplicialcomplexes
3Subdivision
4Simplicialapproximation
5Contiguityclasses
6Theedge-pathgroupoid
7Graphs
8Examplesandapplications
Exercises
4HOMOLOGY
1Chaincomplexes
2Chainhomotopy
3Thehomologyofsimplicialcomplexes
4singularhomotogy
5Exactness
6Mayer-Vietorissequences
7Someapplicationsofhomology
8Axiomaticcharacterizationofhomology
Exercises
5PRODUCTS
1Homologywithcoefficients
2Theuniversal-coefficienttheoremforhomology
3TheKunnethformula
4Cohomology
5Theuniversal-coefficienttheoremforcohomology
6Cupandcapproducts
7Homologyoffiberbundles
8Thecohomologyalgebra
9TheSteenrodsquaringoperations
Exercises
6GENERALCOHOMOLOGYTHEORYANDDUALITY
1Theslantproduct
2Dualityintopologicalmanifolds
3Thefundamentalclassofamanifold
4TheAlexandercohomologytheory
5ThehomotopyaxiomfortheAlexandertheory
6Tautnessandcontinuity
7Presheaves
8Finepresheaves
9Applicationsofthecohomologyofpresheaves
10Characteristicclasses
Exercises
7HOMOTOPYTHEORY
1Exactsequencesofsetsofhomotopyclasses
2Higherhomotopygroups
3Changeofbasepoints
4TheHurewicshonmorphism
5TheHurewiczisomorphismtheorem
6CWcomplexes
7Homotopyfunetors
8Weakhomotopytype
Exercises
8OBSTRUCTIONTHEORY
1Eilenberg-MacLanespaces
2Principalfibrations
3Moore-Postnikovfactorizations
4Obstructiontheory
5Thesuspensionmap
Exercises
9SPECTRALSEQUENCESANDROMOTOPYGROUPSOFSPHERES
1Spectralsequences
2Thespectralsequenceofafibration
3Applicationsofthehomologyspectralsequence
4Multtplicativepropertiesofspectralsequences
5Applicationsofthecohomologyspectralsequence
6Serreclassesofabeltangroups
7Homotopygroupsofspheres
Exercises
INDEX
INTHEMORETHANTWENTYYEARSSINCETHEFIRSTAPPEARANCEOFAlgebraicTopologythebookhasmetwithfavorableresponsebothinitsuseasatextandasareference.Itwasthefirstcomprehensivetreatmentofthefundamentalsofthesubject.Itscontinuingacceptanceatteststothefactthatitscontentandorganizationarestillastimelyaswhenitfirstappeared.Accord-inglyithasnotbeenrevised.
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| 书名 | 代数拓扑站内查询相似图书 | ||
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 59.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
代数拓扑是世界图书出版公司北京公司于2007.10出版的中图分类号为 O189.2 的主题关于 代数拓扑－英文 的书籍。