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1、LECTURESONCHERN-WE11THEORYANDWITTENDEFORMATIONSNankaiTractsinMathematics-Vol.4LECTURESONCHERN-WENTHEORYANDWITTENDEFORMATIONSWeipingZhangNankaiInstituteofMathematicsTionjin,fRChinaWorldScientificewJersey*London*Singapore*HangKongPublishedbyWorldScientificPublishingCo.Pte.Ltd.P0Box128,FanerRoad,Sin
2、gapore912805USAujj5ce:SuiteIB,1060MainStreet,RiverEdge,NJ07661UKofice;57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.LECTURESONCHERN-WEILTHEORYANDWITTENDEFORMATIONSCopyright02001byWorldScientificPub
3、lishingCo.Re.Ltd.Allrightsreserved.Thisbook,orpartsthereoJmaynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pl
4、easepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.ISBN981-02-4685-4ISBN981-02-4686-2(pbk)PrintedinSingapore.DedicatedtomyteachersJean-MichelBismutandShiing-ShenChernPrefaceTheselecturenotesar
5、ebasedonthenotesofagraduatecourseofdifferen-tialgeometryItaughtattheNankaiInstituteofMathematics.Itconsistsoftwoparts:thefirstgeometricpartcontainsanintroductiontothegeo-metrictheoryofcharacteristicclassesduetoShiing-shenChernandAndreWeil,aswellasaproofoftheGauss-Bonnet-CherntheorembasedontheMath
6、ai-QuillenconstructionofThomforms;whilethesecondpart,whichisanalyticinnature,containsanalyticproofsofthePoincark-HopfindexformulaaswellastheMorseinequalitiesbasedondeformationsintroducedbyEdwardWitten.Wehopethisbookcanserveasatextbooktocovermaterialsnotgenerallycontainedinanintroductorycourseindi
7、fferentialgeometry.Withthisreason,wehavenottriedhardtomakethisbookbeingcompletelyself-contained.However,wewillgivedetailedreferenceswhen(possibly)nonstandardresultswillbequoted.Ontheotherhand,wehavetriedtomakeeachchapt
