作者[德]科兹洛夫(Kozlov D) 著
出版社科学出版社
出版时间2011-06
版次1
装帧精装
货号4572
上书时间2022-01-08
商品详情
- 品相描述:八五品
图书标准信息
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作者
[德]科兹洛夫(Kozlov D) 著
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出版社
科学出版社
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出版时间
2011-06
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版次
1
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ISBN
9787030313836
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定价
98.00元
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装帧
精装
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开本
16开
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纸张
胶版纸
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页数
389页
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字数
496千字
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正文语种
英语
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丛书
国外数学名著系列:68
- 【内容简介】
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《组合代数拓扑》是Springer的AlgorithmsandComputationinMathematics丛书系列第21卷,作者多年来从事离散数学,代数拓扑,理论计算机科学。组合代数拓扑是代数拓扑和离散数学的交叉。属于"反映学术前沿进展的优秀学术著作"这一类。比较专门,《组合代数拓扑》的读者可以是几何,拓扑和代数方向的数学工作者和研究生。
- 【目录】
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1Overture
PartIConceptsofAlgebraicTopology
2CellComplexes
2.1AbstractSimplicialComplexes
2.1.1DefinitionofAbstractSimplicialComplexesandMapsBetweenThem
2.1.2Deletion,Link,Star,andWedge
2.1.3SimplicialJoin
2.1.4FacePosets
2.1.5BarycentricandStellarSubdivisions
2.1.6PullingandPushingSimplicialStructures
2.2PolyhedralComplexes
2.2.1GeometryofAbstractSimplicialComplexes
2.2.2GeometricMeaningoftheCombinatorialConstructions
2.2.3GeometricSimplicialComplexes
2.2.4ComplexesWhoseCellsBelongtoaSpecifiedSetofPolyhedra
2.3Trisps
2.3.1ConstructionUsingtheGluingData
2.3.2ConstructionsInvolvingTrisps
2.4CWComplexes
2.4.1GluingAlongaMap
2.4.2ConstructiveandIntrinsicDefinitions
2.4.3PropertiesandExamples
3HomologyGroups
3.1BettiNumbersofFiniteAbstractSimplicialComplexes
3.2SimplicialHomologyGroups
XContents
3.2.1HomologyGroupsofTrispswithCoefficientsinZ2
3.2.2Orientations
3.2.3HomologyGroupsofTrispswithIntegerCoefficients
3.3InvariantsConnectedtoHomologyGroups
3.3.1BettiNumbersandTorsionCoefficients
3.3.2EulerCharacteristicandtheEuler-Poincar6Fc'rmula
3.4Variations
3.4.1AugmentationandReducedHomologyGroups
3.4.2HomologyGroupswithOtherCoefficients
3.4.3SimplicialCohomologyGroups
3.4.4SingularHomology
3.5ChainComplexes
3.5.1DefinitionandHomologyofChainComplexes
3.5.2MapsBetweenChainComplexesandInducedMapsonHomology
3.5.3ChainHomotopy
3.5.4SimplicialHomologyandCohomologyintheContextofChainComplexes
3.5.5HomomorphismsonHomologyInducedbyTrispMaps
3.6CellularHomology
3.6.1AnApplicationofHomologywithIntegerCoefficients:WindingNumber
3.6.2TheDefinitionofCellularHomology
3.6.3CellularMapsandPropertiesofCellularHomology
4ConceptsofCategoryTheory
4.1TheNotionofaCategory
4.1.1DefinitionofaCategory.Isomorphisms
4.1.2ExamplesofCategories
4.2SomeStructureTheoryofCategories
4.2.1InitialandTerminalObjects
4.2.2ProductsandCoproducts
4.3Functors
4.3.1TheCategoryCat
4.3.2HomologyandCohomologyViewedasFunctors
4.3.3GroupActionsasFunctors
4.4LimitC0nstructions
4.4.1DefinitionofColimitofaFunctor
4.4.2ColimitsandInfiniteUnions
4.4.3QuotientsofGroupActionsasColimits
4.4.4Limits
4.5CommaCategories
4.5.1ObjectsBelowandAboveOtherObjects
4.5.2TheGeneralConstructionandFurtherExamples
……
PartⅡMethodsofCombinatorialAlgebraicTopology
PartⅢComplexesofGraphHomomorphisms
References
Index
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