孔涅 非交换几何（ncg）

《孔涅 非交换几何（ncg）》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、NoncommutativeGeometryAlainConnesContentsPreface6Introduction71.Measuretheory(ChaptersIandV)82.TopologyandK-theory(ChapterII)143.Cycliccohomology(ChapterIII)194.Thequantizedcalculus(ChapterIV)255.Themetricaspectofnoncommutativegeometry34Chapter1.NoncommutativeSpacesan

2、dMeasureTheory391.HeisenbergandtheNoncommutativeAlgebraofPhysicalQuantities402.StatisticalStateofaMacroscopicSystemandQuantumStatisticalMechanics453.ModularTheoryandtheClassi¯cationofFactors484.GeometricExamplesofvonNeumannAlgebras:MeasureTheoryofNoncommutativeSpaces5

3、15.TheIndexTheoremforMeasuredFoliations64AppendixA:TransverseMeasuresandAveragingSequences77AppendixB:AbstractTransverseMeasureTheory78AppendixC:NoncommutativeSpacesandSetTheory79Chapter2.TopologyandK-Theory841.C¤-algebrasandtheirK-theory862.ElementaryExamplesofQuotie

4、ntSpaces903.TheSpaceXofPenroseTilings944.DualsofDiscreteGroupsandtheNovikovConjecture995.TheTangentGroupoidofaManifold1046.Wrong-wayFunctorialityinK-theoryasaDeformation1117.TheOrbitSpaceofaGroupAction1168.TheLeafSpaceofaFoliation1239.TheLongitudinalIndexTheoremforFol

5、iations13410.TheAnalyticAssemblyMapandLieGroups141AppendixA:C¤-modulesandStrongMoritaEquivalence156AppendixB:E-theoryandDeformationsofAlgebras163AppendixC:CrossedProductsofC¤-algebrasandtheThomIsomorphism1753CONTENTS4AppendixD:PenroseTilings179Chapter3.CyclicCohomolog

6、yandDi®erentialGeometry1831.CyclicCohomology1872.Examples2123.PairingofCyclicCohomologywithK-Theory2294.TheHigherIndexTheoremforCoveringSpaces2385.TheNovikovConjectureforHyperbolicGroups2446.FactorsofTypeIII,CyclicCohomologyandtheGodbillon-VeyInvariant2507.TheTransver

7、seFundamentalClassforFoliationsandGeometricCorollaries269AppendixA.TheCyclicCategory¤280AppendixB.LocallyConvexAlgebras290AppendixC.StabilityunderHolomorphicFunctionalCalculus291Chapter4.QuantizedCalculus2931.QuantizedDi®erentialCalculusandCyclicCohomology2982.TheDixm

8、ierTraceandtheHochschildClassoftheCharacter3053.QuantizedCalculusinOneVariableandFractalSets3204.ConformalManifolds3395.Fred