非交换几何

图书标准信息

• 作者 [法]孔涅（Connes A.） 著
• 出版社 世界图书出版公司
• 出版时间 2008-06
• 版次 1
• ISBN 9787506292160
• 定价 120.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 661页
• 正文语种 英语
• 原版书名 Noncommutative Geometry

【内容简介】

　　hisbookistheEnglishversionoftheFrench“Geometrienoncommutative”publishedbyInterEditionsParis（1990）.AftertheexcellentinitialtranslationbyS.K.Berberian,aconsiderableamountofrewritingwasdoneandmanyadditionsmade,multiplyingby3.8thesizeoftheoriginalmanuscript.Inparticularthepresenttextcontainsseveralunpublishedresults.

【目录】

TABIFOFCONTENTS
PREFACE
INTRODUCTION
ⅠNONCOMMUTATIVESPACESANDMEASURETHEORY
1.HeisenbergandtheNoncommutativeAlgebraofPhysicalQuantitiesAssociatedtoaMicroscopicSystem
2.StatisticalStateofaMacroscopicSystemandQuantumStatisticalMechanics
3.ModularTheoryandtheClassificationofFactors
4.GeometricExamplesofyonNeumannAlgebras：MeasureTheoryofNoncommutativeSpaces
αClassicalLebesguemeasuretheory
β.Foliations
γ.ThevonNeumannalgebraofafoliation
5.TheIndexTheoremforMeasuredFoliations
α.Transversemeasuresforfollations
β.TheRuelle-SullivancycleandtheELdernumberofameasuredfoliation
γ.TheIndextheoremformeasuredfoliations
A.Appendix：TransverseMeasuresandAveragingSequences
B.AppendL，cAbstractTransverseMeasureTheory
C.Appendix：NoncommutativeSpacesandSetTheory

ⅡTOPOLOGYANDK-THEORY..
1.C*-algebrasandtheirK-theory
2.ElementaryExamplesofQuotientSpaces
α.Opencoversofmanifolds
β.ThedualoftheinfinitedihedralgroupF=Z>~~Z/2
3.TheSpaceXofPenroseTilings
4.DualsofDiscreteGroupsandtheNovikovConjecture
5.TheTangentGroupoidofaManifold
6.Wrong-wayFunctorialityinK-theoryasaDeformation
α.Theindexgroupoidofalinearmap
β.Constructionoff！~~E（T*M~~f*TN，N）
γ.K-orientationsofvectorbundlesandmaps
δ.Wrong-wayfunctorialityforK-orientedmaps
7.TheOrbitSpaceofaGroupAction
8.TheLeafSpaceofaFoliation
α.ConstructionofC*（V，F）
β.ClosedtransversalsandidempotentsofC*（V，F）
γ.Theanalyticassemblymap/~~：K.，r（BG）-.K（C*（V，F））...
9.TheLongitudinalIndexTheoremforFoliations
α.Constructionoflnd（D）~~Ko（J）
β.SignificanceoftheC*-algebraIndex
γ.Thelongitudinalindextheorem
10.TheAnalyticAssemblyMapandLieGroups
α.Geometriccyclesforsmoothgroupoids
β.Liegroupsanddeformations
γ.TheG-equivariantindexofellipticoperatorsonhomogeneousspacesofLiegroups
δ.TheK-theoryK（C*（G））forLiegroups
ε.Thegeneralconjectureforsmoothgroupoids
A.Appendix：C*-modulesandStrongMoritaEquivalence
B.Appendix：E-theoryandDeformationsofAlgebras
α.DeformationsofC*-algebrasandasymptoticmorphisms
β.Compositionofasymptoticmorphisms
γ.AsymptoticmorphismsandexactsequencesofC*-algebras
δ.Theconeofamapandhalf-exactness
ε.E-theory
C.Appendix：CrossedProductsofC*-algebrasandtheThornIsomorphism
D.Appendix：PenroseTilings

ⅢCYCLICCOHOMOLOGYANDDIFFERENTIALGEOMETRY
1.CyclicCohomology
α.CharactersofcyclesandthecupproductinHC*
β.CobordismsofcyclesandtheoperatorB
γ.TheexactcouplerelatingHC*（A）toHochschildcohomology
2.Examples
α.A=C（V），Vacompactsmoothmanifold
β.ThecycliccohomologyofthenoncommutativetorusA=Aθ1θεR/Z
γ.ThecycliccohomologyofthegroupringCFforFadiscretegroup
δ.CycliccohomologyofC（V>F）
3.PairingofCyclicCohomologywithK-Theory
4.TheHigherIndexTheoremforCoveringSpaces
α.Thesmoothgroupoidofacoveringspace
β.ThegroupringRF
γ.Theindextheorem
5.TheNovikovConjectureforHyperbolicGroups
α.Wordhyperbolicgroups
β.TheHaagerupinequality
γ.ExtensiontoC*（F）ofK-theoryinvariants
6.FactorsofTypeIII，CyclicCohomologyandtheGodbillon-Veylnvariant
α.ExtensionofdenselydefinedcycliccocyclesonBanachalgebras
β.TheBott-ThurstoncocycleandtheequaliWGV=i[V/F]
γ.Invariantmeasuresontheflowofweights
7.TheTransverseFundamentalClassforFoliationsandGeometricCorollaries
α.Thetransversefundamentalclass
β.Geometriccorollaries
γ.Indexformulaforlongitudinalellipticoperators
A.Appendix：TheCyclicCategoryA
α.Thesimplicialcategory
β.Thecycliccategory
γ.TheA-moduleAassociatedtoanalgebraA
δ.Cyclicspacesand$1spaces
B.Appendix：LocallyConvexAlgebras
C.Appendix：StabiliWunderHolomorphicFunctionalCalculus

ⅣQUANTIZEDCALCULUS
1.QuantizedDifferentialCalculusandCyclicCohomology
a.ThecycleassociatedtoaFredholmmodule
β.TheperiodicityoperatorSandtheCherncharacter
r.PairingwithK-theoryandindexformula
2.TheDixmlerTraceandtheHochschiidClassoftheCharacter
a.Generalpropertiesofinterpolationideals
β.TheDlxmiertrace
γ.TheresidueformulafortheHochschildclassofthecharacterofFredholmmodules
δ.GrowthofalgebrasanddegreeofsummabilityofK-cycles
ε.QuantizedCalculusmOneVariableandFractalSets
a.Quantizedcalculusinonevariable
β.Theclassofdfin
γ.TheDixmiertraceoff（Z）｜dZ｜p
δ.Theharmonicmeasureandnon-normalityoftheDlxmlertrace
ε.Cantorsets，DixrniertraceandMinkowsldmeasure
4.ConformalManifolds
a.Quantizedcalculusonconformalmanifolds
β.PerturbationofFredholmmodulesbythecommutantvonNeumannalgebra
γ.The4-dimensionalanalogueofthePolyakovaction
5.FredholmModulesandRank-OneDiscreteGroups
6.EllipticTheoryontheNoncommutativeTorusandtheQuantumHallEffect
a.Elliptictheoryon
β.ThequantumHalleffect
γ.TheworkofJ.Bellissardontheintegralityof（rH
7.EntireCyclicCohomology
α.EntirecycliccohomologyofBanachalgebras
β.Infinite-dimensionalcycles
γ.TracesonQAandΕA
δ.PairingwithKo（A）
ε.EntirecycliccohomologyofS1
8.TheChernCharacterofθ-summableFredholmModules
α.FredholmmodulesandK-cycles
β.ThesupergroupR1，1andtheconvolutionalgebraofoperator-valueddistributionson
γ.TheCherncharacterofK-cycles
δ.Theindexformula
ε.TheJLOcocycle
9.θ-summableK-cycles，DiscreteGroupsandQuantumFieldTheory
αDiscretesubgroupsofLiegroups
β.Supersymmetr/cquantumfieldtheory
A.Appendix：KasparovsBivariantTheory
B.Appendix：RealandComplexInterpolationofBanachSpaces
C.Appendix：NonnedIdealsofCompactOperators
D.Appendix：TheChernCharacterofDeformationsofAlgebras

ⅤOPERATORALGEBRAS
1.ThePapersofMurrayandyonNeumann
α.ExamplesofyonNeumannalgebras
β.Reductiontheory
γ.Comparisonofsubrepresentations，comparisonofprojectionsandtherelativedimensionfunction
δ.Algebraicisomorphismandspatialisomorphism
ε.TheKrsttwoexamplesoftypeII1factors，thehyperfinitefactorandthepropertyF
2.RepresentationsofC*-algebras
3.TheAlgebraicFrameworkforNoncommutativeIntegrationandtheTheoryofWeights
4.TheFactorsofPowers，AraldandWoods，andofKrieger
5.TheRadon-NtkodynTheoremandFactorsofTypeHI~~
αTheRadon-Nikodymtheorem
β.ThefactorsoftypeIIIλ
6.NoncommutativeErg0dicTheory
α.Rokhlinstheorem
β.Entropy
γ.Approximatelyinnerautomorphisms
δ.Centrallytrivialautomorphisms
ε.Theobstructionγ（θ）
ζ.ThelistofautomorphismsofRuptoouterconjugacy
η.AutomorphismsoftheAraki-WoodsfactorR0，1oftype
7.AmenableyonNeumannAlgebras
α.Approximationbyfinite-dimensionalalgebras
β.ThepropertiesPofSchwartz，EofHakedaandTomiyama，andinjectivity
γ.SemidiscretevonNeumannalgebras
8.TheFlowofWeights：mod（M）
a.ThediscretedecompositionoffactorsoftypeIIIO
β.ContinuousdecompositionoftypeIIlfactors
γ.Functorialdefinitionoftheflowofweights
ⅥTHEMETRICASPECTOFNONCOMMUTATIVEGEOMETRY~