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《bryant r.l. introduction to lie groups and symplectic geometry (1993 lectures)(170s)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、AnIntroductiontoLieGroupsandSymplecticGeometryAseriesofninelecturesonLiegroupsandsymplecticgeometrydeliveredattheRegionalGeometryInstituteinParkCity,Utah,24June–20July1991.byRobertL.BryantDukeUniversityDurham,NCbryant@math.duke.eduThisisanunofficialversionofthenotesand
2、waslastmodifiedon20September1993.The.dvifileforthispreprintwillbeavailablebyanonymousftpfrompublications.math.duke.eduinthedirectorybryantuntilthemanuscriptisacceptedforpublication.YoushouldgettheReadMefilefirsttoseeiftheversionthereismorerecentthanthisone.Pleasesendanyc
3、omments,correctionsorbugreportstotheabovee-mailaddress.IntroductionThesearethelecturenotesforashortcourseentitled“IntroductiontoLiegroupsandsymplecticgeometry”whichIgaveatthe1991RegionalGeometryInstituteatParkCity,Utahstartingon24Juneandendingon11July.Thecoursereally
4、wasdesignedtobeanintroduction,aimedatanaudienceofstu-dentswhowerefamiliarwithbasicconstructionsindifferentialtopologyandrudimentarydifferentialgeometry,whowantedtogetafeelforLiegroupsandsymplecticgeometry.MypurposewasnottoprovideanexhaustivetreatmentofeitherLiegroups,w
5、hichwouldhavebeenimpossibleevenifIhadhadanentireyear,orofsymplecticmanifolds,whichhaslatelyundergonesomethingofarevolution.Instead,ItriedtoprovideanintroductiontowhatIregardasthebasicconceptsofthetwosubjects,withanemphasisonexampleswhichdrovethedevelopmentofthetheory
6、.Ideliberatelytriedtoincludeafewtopicswhicharenotpartofthemainstreamsubject,suchasLie’sreductionoforderfordifferentialequationsanditsrelationwiththenotionofasolvablegroupontheonehandandintegrationofODEbyquadratureontheother.Ialsotried,inthelaterlecturestointroducether
7、eadertosomeoftheglobalmethodswhicharenowbecomingsoimportantinsymplecticgeometry.However,afulltreatmentofthesetopicsinthespaceofninelecturesbeginningattheelementarylevelwasbeyondmyabilities.Afterthelectureswereover,Icontemplatedreworkingthesenotesintoacomprehen-sivein
8、troductiontomodernsymplecticgeometryand,aftersomesoul-searching,finallydecidedagainstthis.Thus,Ihavecontentedmyselfwithmakingonlymin
