Foundations of Differential Geometry - P. Michor

《Foundations of Differential Geometry - P. Michor》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、FOUNDATIONSOFDIFFERENTIALGEOMETRYPeterW.MichorMailingaddress:PeterW.Michor,InstitutfurMathematikderUniversitatWien,Strudlhofgasse4,A-1090Wien,Austria.E-mailmichor@awirap.bitnetThesenotesarefromalecturecourseDierentialgeometrieundLieGruppenwhichhasbeenheldattheUniversityofViennaduringtheaca

2、demicyear1990/91,againin1994/95,andinWS1997.Itisnotyetcompleteandwillbeenlargedduringtheyear.InthislecturecourseIgivecompletedenitionsofmanifoldsinthebeginning,but(besidespheres)examplesaretreatedextensivelyonlylaterwhenthetheoryisdevelopedenough.Iadviseeverynovicetotheeldtoreadtheexcellen

3、tlecturenotesTypesetbyAS-TXMEiiTABLEOFCONTENTS1.DierentiableManifolds.....................12.SubmersionsandImmersions..................133.VectorFieldsandFlows....................184.LieGroupsI.........................395.LieGroupsII.LieSubgroupsandHomogeneousSpaces.......556.VectorBundles.

4、.......................647.DierentialForms.......................768.IntegrationonManifolds....................849.DeRhamcohomology.....................9110.CohomologywithcompactsupportsandPoincareduality......................10211.DeRhamcohomologyofcompactmanifolds...........11712.Liegrou

5、psIII.AnalysisonLiegroups..............12413.DerivationsontheAlgebraofDierentialFormsandtheFrolicher-NijenhuisBracket...............13714.FiberBundlesandConnections.................14615.PrincipalFiberBundlesandG-Bundles.............15716.PrincipalandInducedConnections...............17517.C

6、haracteristicclasses.....................19618.Jets.............................212References............................219ListofSymbols.........................222Index..............................224DraftfromNovember17,1997PeterW.Michor,11.DierentiableManifolds1.1.Manifolds.Atopological

7、manifoldisaseparablemetrizablespaceMnwhichislocallyhomeomorphictoR.Soforanyx2Mthereissomehomeo-nmorphismu:U!u(U)R,whereUisanopenneighborhoodofxinMandnu(U)isanopensubsetinR.Thepair(Uu)iscalledachartonM.Fromalgebraictopologyitfollowsthatthenumberni