组合代数拓扑

图书标准信息

• 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
• ISBN 9787030313836
• 定价 98.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 389页
• 字数 496千字
• 正文语种 英语
• 丛书 国外数学名著系列：68

【内容简介】

《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】

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