introduction to characteristic classes and index theory

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1、TEXTOSDEMATEMATICAINTRODUCTIONTOCHARACTERISTICCLASSESANDINDEXTHEORYJean-PierreSchneiderswX(EReTXF=)=w:[
])(E)^#([
]w)=(F(X)(X;OTXX(Dtd))^=FdegRchD=X+)1;Fg(XUNIVERSIDADEDELISBOAFaculdadedeCi^enciasDepartamentodeMatematicaTextosdeMatematica,Volume13,DepartamentodeMatematicaFaculdade

2、deCi^enciasdaUniversidadedeLisboa,2000Editores:FernandoC.SilvaeL.TrabuchoTtulo:IntroductiontoCharacteristicClassesandIndexTheoryAutor:Jean-PierreSchneidersISBN:972-8394-12-8INTRODUCTIONTOCHARACTERISTICCLASSESANDINDEXTHEORYJean-PierreSchneidersUNIVERSIDADEDELISBOAFaculdadedeCi^enciasDepar

3、tamentodeMatematica2000Author'saddress:LaboratoireAnalyse,GeometrieetApplications(UMR7539)InstitutGalilee,UniversiteParis13AvenueJean-BaptisteClementF-93430Villetaneuse,FranceE-mail:jps@math.univ-paris13.frURL:MathematicsSubjectClassication(2000

4、):55R40,57R20,19L10,14C40.PrefaceThisbookisbasedonacoursegivenbytheauthorattheuniversityofLisbonduringtheacademicyear1997{1998.Thiscoursewasdividedinthreepartsdealingrespectivelywithcharacteristicclassesofrealandcom-plexvectorbundles,Hirzebruch-Riemann-RochformulaandAtiyah-Singertheorem.In

5、thetextwhichfollows,wehavedecidedtotreatonlythersttwosubjects.Foranintroductiontothelastone,wereferthereaderto[21]fortheclassicalpointofvieworto[22,23]forrecentdevelopments.ThetheoryofcharacteristicclassesisaverywelldevelopedbranchofmathematicsandtheliteratureconcerningRiemann-Rochtheorem

6、ishuge.So,wewillnottrytogiveafullviewofthesesubjects.Wewillratherpresentafewbasicbutfundamentalfactswhichshouldhelpthereadertogainagoodideaofthemathematicsinvolved.Althoughthereaderisassumedtohaveagoodknowledgeofhomologicalalgebraandtopology,webeginwithachaptersurveyingtheresultsofsheafthe

7、orywhichareneededintherestofthebook.Inparticularwerecallresultsconcerningacyclicsheaves,tautsubspaces,Poincare-VerdierdualityandBorel-Moorehomology,illustratingthembymeansofexamplesandexercises.Wereferthereaderwhowouldlikeamoredetailedtreatmentofthisparttosta