热核与狄拉克算子（英文版）

图书标准信息

• 作者 波林 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787506292139
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 其他
• 页数 363页
• 正文语种 英语

【内容简介】

　　Thisbook，whichbeganasaseminarin1985atMIT，containscompleteproofsofthelocalindextheoremforDiracoperatorsusingtheheatkernelapproach，togetherwithitsgeneralizationstoequivariantDiracoperatorsandfamiliesofDiracoperators，aswellasbackgroundmaterialonsuperconnectionsandequivariantdifferentialforms.
　　Sincethepublicationofthefirstedition，thesubjectstreatedherehavecontin-uedtofindnewapplications.Equivariantcohomologyplaysanimportantroleinthestudyofsymplecticreduction，andBismutsuperconnectionsandthelocalindexthe-oremforfamilieshavehadmanyapplications，throughtheconstructionofhigheranalytictorsionformsandcurrents.（Forasurveyofsomeofthesedevelopments，werecommendreadingBismutstalkattheBerlinInternationalCongressofMathe-maticians，reference
　　Althoughthisbooklackssomeoftheusualattributesofatextbook（suchasexercises），ithasbeenwidelyusedinadvancedcoursesindifferentialgeometry;formanyofthetopicsdiscussedhere，therearenoothertreatmentsavailableinmonographform.Becauseofthecontinuingdemandfromstudentsforthebook，wewerevery

【目录】

Introduction
1BackgroundonDifferentialGeometry
1.1FibreBundlesandConnections
1.2RiemannianManifolds
1.3Superspaces
1.4Superconnections
1.5CharacteristicClasses
1.6TheEulerandThornClasses

2AsymptoticExpansionoftheHeatKernel
2.1DifferentialOperators
2.2TheHeatKernelonEuclideanSpace
2.3HeatKernels
2.4ConstructionoftheHeatKernel
2.5TheFormalSoLution
2.6TheTraceoftheHeatKernel
2.7HeatKernelsDependingonaParameter

3CLiffordModulesandDiraeOperators
3.1TheCliffordAlgebra
3.2Spinors
3.3DiracOperators
3.4IndexofDiracOperators
3.5TheLichnerowiczFormula
3.6SomeExamplesofCliffordModules

4IndexDensityofDiracOperators
4.1TheLocalIndexTheorem
4.2MehlersFormula
4.3CalculationoftheIndexDensity
5TheExponentialMapandtheIndexDensity
5，1IacobianoftheExponentialMaponPrincipalBundles
5.2TheHeatKernelofaPrincipalBundle
5.3CalculuswithGrassmannandCliffordVariables
5.4TheIndexofDiracOperators

6TheEquivariantIndexTheorem
6.1TheEquivariantIndexofDiracOperators
6.2TheAtiyah-BottFixedPointFormula
6.3AsymptoticExpansionoftheEquivariantHeatKernel
6.4TheLocalEquivariantIndexTheorem
6.5GeodesicDistanceonaPrincipalBundle
6.6Theheatkernelofanequivariantvectorbundle
6.7ProofofProposition6.13

7EquivariantDifferentialForms
7.1EquivariantCharacteristicClasses
7.2TheLocalizationFormula
7.3BottsFormulasforCharacteristicNumbers
7.4ExactStationaryPhaseApproximation
5TheFourierTransformofCoadjointOrbits
7.6EquivariantCohomologyandFamilies
7.7TheBottClass

8TheKirillovFormulafortheEquivariantIndex
8.1TheKirillovFormula
8.2TheWeylandKirillovCharacterFormulas
8.3TheHeatKernelProofoftheKirillovFormula

9TheIndexBundle
9.1TheIndexBundleinFiniteDimensions
9.2TheIndexBundleofaFamilyofDiracOperators
9.3TheChernCharacteroftheIndexBundle
9.4TheEquivariantIndexandtheIndexBundle
9.5TheCaseofVaryingDimension
9.6TheZeta-FunctionofaLaplacian
9.7TheDeterminantLineBundle

10TheFamilyIndexTheorem
10.1RiemannianFibreBundles
10.2CliffordModulesonFibreBundles
10.3TheBismutSuperconnection
10.4TheFamilyIndexDensity
10.5TheTransgressionFormula
10.6TheCurvatureoftheDeterminantLineBundle
10.7TheKirillovFormulaandBismutsIndexTheorem