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莫尔斯理论入门

莫尔斯理论入门

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作者: [美] 尼古莱斯库著

出版社: 世界图书出版公司

出版时间: 2010-09

版次: 1

ISBN: 9787510027291

定价: 35.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 241页

正文语种: 英语

分类: 自然科学

18人买过

Asthethetitlesuggests，thegoalofthisbookistogivethereaderatasteofthe“unreasonableeffectiveness”ofMorsetheory.Themainideabehindthistechniquecanbeeasilyvisualized.
SupposeMisasmooth，compactmanifold，whichforsimplicityweas-sumeisembeddedinaEuclideanspaceE.WewouldliketounderstandbasictopologicalinvariantsofMsuchasitshomology，andweattempta“slicing”technique. Preface
Notationsandconventions
1MorseFunctions
1.1TheLocalStructureofMorseFunctions
1.2ExistenceofMorseFunctions

2TheTopologyofMorseFunctions
2.1Surgery，HandleAttachment.andCobordisms
2.2TheTopologyofSublevelSets
2.3MorseInequalities
2.4Morse-SmaleDynamics
2.5Morse-FloerHomology
2.6Morse-BottFunctions
2.7Min-MaxTheory

3Applications
3.1TheCohomologyofComplexGrassmannians
3.2LefschetzHyperplaneTheorem
3.3SymplecticManifoldsandHamiltonianFlows
3.4MorseTheoryofMomentMaps
3.5S1-EquivariantLocalization

4BasicsofCompleXMorseTheory
4.1SomeFundamentalConstructions
4.2TopologicalApplicationsofLefschetzPencils
4.3TheHardLefschetzTheorem
4.4VanishingCyclesandLocalMonodromy
4.5ProofofthePicardLefschetzformula
4.6GlobalPicard-LefschetzFormulae

5ExercisesandSolutions
5.1Exercises
5.2SolutionstoSelectedExercises
References
Index
内容简介:
Asthethetitlesuggests，thegoalofthisbookistogivethereaderatasteofthe“unreasonableeffectiveness”ofMorsetheory.Themainideabehindthistechniquecanbeeasilyvisualized.
SupposeMisasmooth，compactmanifold，whichforsimplicityweas-sumeisembeddedinaEuclideanspaceE.WewouldliketounderstandbasictopologicalinvariantsofMsuchasitshomology，andweattempta“slicing”technique.
目录:
Preface
Notationsandconventions
1MorseFunctions
1.1TheLocalStructureofMorseFunctions
1.2ExistenceofMorseFunctions

2TheTopologyofMorseFunctions
2.1Surgery，HandleAttachment.andCobordisms
2.2TheTopologyofSublevelSets
2.3MorseInequalities
2.4Morse-SmaleDynamics
2.5Morse-FloerHomology
2.6Morse-BottFunctions
2.7Min-MaxTheory

3Applications
3.1TheCohomologyofComplexGrassmannians
3.2LefschetzHyperplaneTheorem
3.3SymplecticManifoldsandHamiltonianFlows
3.4MorseTheoryofMomentMaps
3.5S1-EquivariantLocalization

4BasicsofCompleXMorseTheory
4.1SomeFundamentalConstructions
4.2TopologicalApplicationsofLefschetzPencils
4.3TheHardLefschetzTheorem
4.4VanishingCyclesandLocalMonodromy
4.5ProofofthePicardLefschetzformula
4.6GlobalPicard-LefschetzFormulae

5ExercisesandSolutions
5.1Exercises
5.2SolutionstoSelectedExercises
References
Index

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