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[美]尼古莱斯库 著 / 世界图书出版公司 / 2010-09 / 平装
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莫尔斯理论入门
Asthethetitlesuggests,thegoalofthisbookistogivethereaderatasteofthe“unreasonableeffectiveness”ofMorsetheory.Themainideabehindthistechniquecanbeeasilyvisualized.
SupposeMisasmooth,compactmanifold,whichforsimplicityweas-sumeisembeddedinaEuclideanspaceE.WewouldliketounderstandbasictopologicalinvariantsofMsuchasitshomology,andweattempta“slicing”technique.
PrefaceNotationsandconventions1MorseFunctions1.1TheLocalStructureofMorseFunctions1.2ExistenceofMorseFunctions2TheTopologyofMorseFunctions2.1Surgery,HandleAttachment.andCobordisms2.2TheTopologyofSublevelSets2.3MorseInequalities2.4Morse-SmaleDynamics2.5Morse-FloerHomology2.6Morse-BottFunctions2.7Min-MaxTheory3Applications3.1TheCohomologyofComplexGrassmannians3.2LefschetzHyperplaneTheorem3.3SymplecticManifoldsandHamiltonianFlows3.4MorseTheoryofMomentMaps3.5S1-EquivariantLocalization4BasicsofCompleXMorseTheory4.1SomeFundamentalConstructions4.2TopologicalApplicationsofLefschetzPencils4.3TheHardLefschetzTheorem4.4VanishingCyclesandLocalMonodromy4.5ProofofthePicardLefschetzformula4.6GlobalPicard-LefschetzFormulae5ExercisesandSolutions5.1Exercises5.2SolutionstoSelectedExercisesReferencesIndex
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