Springer.Guillemin.Sternberg_Supersymmetry.and.equivariant.de.Rham.theory.(1999)(128s)

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1、VictorW.GuilleminShlomoSternbergSupersymmetryandEquivariantdeRhamTheoryPrefaceThisisthesecondvolumeoftheSpringercollectionMathematicsPastandPresent.Inthefirstvolume,werepublishedHormander'sfundamentalpapersFourierintegraloperntorstogetherwithabriefintroductionwritt

2、enfromtheperspectiveof1991.Thecompositionofthesecondvolumeissomewhatdifferent:thetwopapersofCartanwhicharereproducedherehaveatotallengthoflessthanthlrtypages,andthe220pageintroductionwhichprecedesthemisintendednotonlyasacommentaryonthesepapersbutasatextbookofitsown

3、,onafascinatingareaofmathematicsinwhichalotofexcitinginnovatiopshaveoccurredinthelastfewyears.Thus,inthissecondvolumetherolesofthereprintedtextanditscommentaryarereversed.TheseminalideasoutlinedinCartan'stwopapersaretakenasthepointofdepartureforafullmoderntreatment

4、ofequivariantdeRhamtheorywhichdoesnotyet.existintheliterature.Weenvisagethatfuturevolumesinthiscollectionwillrepresentbothvari-antsoftheinterplaybetweenpastandpresentmathematics:wewillpublishclassicaltexts,stillofvitalinterest,eitherreinterpretedagainsttheback-grou

5、ndoffullydevelopedtheoriesortakenastheinspirationfororiginaldevelopments.ContentsIntroductionxiii1EquivariantCohomologyinTopology11.1EquivariantCohomologyviaClassifyingBundles......11.2ExistenceofClassifyingSpaces................51.3BibliogaphicalNotesforChapter1..

6、............62GYModules2.1Differential-GeometricIdentities................2.2TheLanguageofSuperdgebra.................2.3FromGeometrytoAlgebra...................2.3.1Cohomology.......................2.3.2Acyclicity........................2.3.3ChainHomotopies.......

7、............2.3.4FreeActionsandtheCondition(C)..........2.3.5TheBasicSubcomplex.................2.4EquivariantCohomologyofG*Algebras...........2.5TheEquivariantdeRhamTheorem..............2.6BibliographicdNotesforChapter2..............3TheWeilAlgebra333.1TheKoszulCo

8、mplex......................333.2TheWeilAlgebra........................343.3ClassifymgMaps........................373.4W*Modules..................