矩映射、配边和Hamilton群作用 (美)维克多·吉耶曼,(美)维克多·金兹伯格,(加)耶尔·卡尔松 著 专业科技

Chapter 1.Introduction
1.Topological aspects of Hamiltonian group actions
2.Hamiltonian cobordism
3.The linearization theorem and non-compact cobordisms
4.Abstract moment maps and non-degeneracy
5.The quantum linearization theorem and its applications
6.Acknowledgements
Part 1.Cobordism
Chapter 2.Hamiltonian cobordism
1.Hamiltonian group actions
2.Hamiltonian geometry
3.Compact Hamiltonian cobordisms
4.Proper Hamiltonian cobordisms
5.Hamiltonian complex cobordisms
Chapter 3.Abstract moment maps
1.Abstract moment maps: definitions and examples
2.Proper abstract moment maps
3.Cobordism
4.First examples of proper cobordisms
5.Cobordisms of surfaces
6.Cobordisms of linear actions
Chapter 4.The linearization theorem
1.The simplest case of the linearization theorem
2.The Hamiltonian linearization theorem
3.The linearization theorem for abstract moment maps
4.Linear torus actions
5.The right-hand side of the linearization theorems
6.The Duistermaat-Heckman and Guillemin-Lerman-Sternberg formulas
Chapter 5.Reduction and applications
1.(Pre-)symplectic reduction
2.Reduction for abstract moment maps
3.The Duistermaat-Heckman theorem
4.Kaihler reduction
5.The complex Delzant construction
6.Cobordism of reduced spaces
7.Jeffrey-Kirwan localization
8.Cutting
Part 2.Quantization
Chapter 6.Geometric quantization
1.Quantization and group actions
2.Pre-quantization
3.Pre-quantization of reduced spaces
4.Kirillov-Kostant pre-quantization
5.Polarizations, complex structures, and geometric quantization
6.Dolbeault Quantization and the Riemann-Roch formula
7.Stable complex quantization and Spinc quantization
8.Geometric quantization as a push-forward
Chapter 7.The quantum version of the linearization theorem
1.The quantization of Cd
2.Partition functions
3.The character of Q(Ca)
4.A quantum version of the linearization theorem
Chapter 8.Quantization commutes with reduction
1.Quantization and reduction commute
2.Quantizatioa of stable complex toric varieties
3.Linearization of [Q,R]=0
4.Straightening the symplectic and complex structures
5.Passing to holomorphic sheaf cohomology
6.Computing global sections; the lit set
7.The Cech complex
8.The higher cohomology
9.Singular [Q,R]=0 for non-symplectic Hamiltonian G-manifolds
10.Overview of the literature
Part 3.Appendices
Appendix A.Signs and normalization conventions
1.The representation of G on C∞(M)
2.The integral weight lattice
3.Connection and curvature for principal torus bundles
4.Curvature and Chern classes
5.Equivariant curvature; integral equivariant cohomology
Appendix B.Proper actions of Lie groups
1.Basic definitions
2.The slice theorem
3.Corollaries of the slice theorem
4.The Mostow-Palais embedding theorem
5.Rigidity of compact group actions
Appendix C.Equivariant cohomology
1.The definition and basic properties of equivariant cohomology
2.Reduction and cohomology
3.Additivity and localization
4.Formality
5.The relation between H* G and H* T
6.Equivariant vector bundles and characteristic classes
7.The Atiyah-Bott-Berline-Vergne localization formula
8.Applications of the Atiyah-Bott-Berline-Vergne localization formula
9.Equivariant homology
Appendix D.Stable complex and Spine-structures
1.Stable complex structures
2.Spine-structures
3.Spine-structures and stable complex structures
Appendix E.Assignments and abstract moment maps
1.Existence of abstract moment maps
2.Exact moment maps
3.Hamiltonian moment maps
4.Abstract moment maps on linear spaces are exact
5.Formal cobordism of Hamiltonian spaces
Appendix F.Assignment cohomology
1.Construction of assignment cohomology
2.Assignments with other coefficients
3.Assignment cohomology for pairs
4.Examples of calculations of assignment cohomology
……