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,DepartamentodeMatemati

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

3、uldadedeCi^enciasDepartamentodeMatematica2000Author'saddress:LaboratoireAnalyse,GeometrieetApplications(UMR7539)InstitutGalilee,UniversiteParis13AvenueJean-BaptisteClementF-93430Villetaneuse,FranceE-mail:jps@math.univ-paris13.frURL:Mat

4、hematicsSubjectClassication(2000):55R40,57R20,19L10,14C40.PrefaceThisbookisbasedonacoursegivenbytheauthorattheuniversityofLisbonduringtheacademicyear1997{1998.Thiscoursewasdividedinthreepartsdealingrespectivelywithcharacteristicclassesofrealandcom-plexvectorbundles,Hirzebruch-R

5、iemann-RochformulaandAtiyah-Singertheorem.Inthetextwhichfollows,wehavedecidedtotreatonlythersttwosubjects.Foranintroductiontothelastone,wereferthereaderto[21]fortheclassicalpointofvieworto[22,23]forrecentdevelopments.Thetheoryofcharacteristicclassesisaverywelldevelopedbranchofm

6、athematicsandtheliteratureconcerningRiemann-Rochtheoremishuge.So,wewillnottrytogiveafullviewofthesesubjects.Wewillratherpresentafewbasicbutfundamentalfactswhichshouldhelpthereadertogainagoodideaofthemathematicsinvolved.Althoughthereaderisassumedtohaveagoodknowledgeofhomologicala

7、lgebraandtopology,webeginwithachaptersurveyingtheresultsofsheaftheorywhichareneededintherestofthebook.Inparticularwerecallresultsconcerningacyclicsheaves,tautsubspaces,Poincare-VerdierdualityandBorel-Moorehomology,illustratingthembymeansofexamplesandexercises.Wereferthereaderwh

8、owouldlikeamoredetailedtreatmentofthisparttosta