moment maps, cobordisms, and hamiltonian group actions

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1、Momentmaps,cobordisms,andHamiltoniangroupactionsViktorGinzburgVictorGuilleminYaelKarshonAuthoraddress:DepartmentofMathematics,UniversityofCaliforniaatSantaCruz,SantaCruz,CA95064E-mailaddress:ginzburg@math.ucsc.eduDepartmentofMathematics,MassachusettsInstituteofTechnol-ogy,Cambridge

2、,MA02139E-mailaddress:vwg@math.mit.eduInstituteofMathematics,TheHebrewUniversityofJerusalem,Jerusalem91904,IsraelE-mailaddress:karshon@math.huji.ac.ilContentsChapter1.Introduction11.TopologicalaspectsofHamiltoniangroupactions12.Hamiltoniancobordism43.Thelinearizationtheoremandnon-c

3、ompactcobordisms54.Abstractmomentmapsandnon-degeneracy75.Thequantumlinearizationtheoremanditsapplications86.Acknowledgements10Part1.Cobordism13Chapter2.Hamiltoniancobordism151.Hamiltoniangroupactions152.Hamiltoniangeometry213.CompactHamiltoniancobordisms244.ProperHamiltoniancobordi

4、sms275.Hamiltoniancomplexcobordisms29Chapter3.Abstractmomentmaps311.Abstractmomentmaps:denitionsandexamples312.Properabstractmomentmaps333.Cobordism344.Firstexamplesofpropercobordisms375.Cobordismsofsurfaces396.Cobordismsoflinearactions42Chapter4.Thelinearizationtheorem451.Thesimp

5、lestcaseofthelinearizationtheorem452.TheHamiltonianlinearizationtheorem473.Thelinearizationtheoremforabstractmomentmaps514.Lineartorusactions525.Theright-handsideofthelinearizationtheorems566.TheDuistermaat-HeckmanandGuillemin-Lerman-Sternbergformulas58Chapter5.Reductionandapplicat

6、ions631.(Pre-)symplecticreduction632.Reductionforabstractmomentmaps653.TheDuistermaat{Heckmantheorem694.K•ahlerreduction725.ThecomplexDelzantconstruction736.Cobordismofreducedspaces81vviCONTENTS7.Jerey{Kirwanlocalization828.Cutting84Part2.Quantization87Chapter6.Geometricquantizati

7、on891.Quantizationandgroupactions892.Pre-quantization903.Pre-quantizationofreducedspaces964.Kirillov{Kostantpre-quantization995.Polarizations,complexstructures,andgeometricquantization1026.DolbeaultQuantizationandtheRiemann{Rochformula1107.StablecomplexquantizationandSpincquantizat

8、ion1138.Geometricquantizat