●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
……

Guillemin,Ginzburg和Karshon的研究表明，從隱含的拓撲脈絡來看，G流形不變量的計算是涉及同變配邊的線性化定理的結果。本書呈現了這一當前極受關注的快速發展領域中的許多新的成果，采用了新穎的方法，並展示了令人激動的新研究。在過去的幾十年中，“局部化”一直是同變微分幾何學領域的重要主題之一。典型的結果是Duistermaat-Heckman理論、同變de Rham理論中的Berline-Vergne-Atiyah-Bott局部化定理以及“量化與約化交換”定理及其各種推論。為了闡述這些定理都是涉及同變配邊的單個結論的結果這一想法，作者開發了允許對像是非緊致流形的配邊理論。這種非緊致配邊的關鍵要素是同變幾何對像，他們稱其為“抽像矩映射”。這是在Hamilton動力學理論中出現的矩映射的自然而重要的推廣。本書還包含了多個附錄，內容包括流形上正常群作用、同變上同調、Spinc結構和等