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矩映射、配边和Hamilton群作用（影印版）

样章
作者：
Victor Guillemin, Viktor Ginzburg, Yael Karshon
定价：
169.00 元
版面字数：
580千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2020年
ISBN：
978-7-04-053595-2
物料号：
53595-00
出版时间：
2020-04-20
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
几何学
暂无
  • 目录
    • 前辅文
      • 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
                  • 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.Cobordism s of surfaces
                                        • 6.Cobordism s 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 Duis term a at-Heckman theorem
                                                            • 4.Kahler reduction
                                                              • 5.The complex Del zant construction
                                                                • 6.Cobordism of reduced spaces
                                                                • Chapter 6.Geometric quantization
                                                                  • 1.Quantization and group actions
                                                                    • 2.Pre-quantization
                                                                      • 3.Pre-quantization of reduced spaces
                                                                        • 4.Kirillov-Kosta nt pre-quantization
                                                                          • 5.Polarizations， complex structures，and geometric quantization
                                                                            • 6.Dol be ault Quantization and the Riemann-Roch formula
                                                                              • 7.Stable complex quantization and Spin°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(Cd
                                                                                        • 4.A quantum version of the linearization theorem
                                                                                        • Chapter 8.Quantization commutes with reduction
                                                                                          • 1.Quantization and reduction commute
                                                                                            • 2.Quantization 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
                                                                                                            • Appendix A.Signs and normalization conventions
                                                                                                              • 1.The representation of GonC°(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 therrem
                                                                                                                              • 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*
                                                                                                                                            • 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 Spin°-structures
                                                                                                                                                    • 1.Stable complex structures
                                                                                                                                                      • 2.Spin°-structures
                                                                                                                                                        • 3.Spin-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
                                                                                                                                                                            • 5.Generalizations of assignment cohomology
                                                                                                                                                                            • Appendix G.Non-degenerate abstract moment maps
                                                                                                                                                                              • 1.Definitions and basic examples
                                                                                                                                                                                • 2.Global properties of non-degenerate abstract moment maps
                                                                                                                                                                                  • 3.Existence of non-degenerate two-forms
                                                                                                                                                                                  • Appendix H.Characteristic numbers,non-degenerate cobordisms, and non-virtual quantization
                                                                                                                                                                                    • 1.The Hamiltonian cobordism ring and characteristic classes
                                                                                                                                                                                      • 2.Characteristic numbers
                                                                                                                                                                                        • 3.Characteristic numbers as a full system of invariants
                                                                                                                                                                                          • 4.Non-degenerate cobordisms
                                                                                                                                                                                            • 5.Geometric quantization
                                                                                                                                                                                            • Appendix I.The Kawasaki Riemann-Roch formula
                                                                                                                                                                                              • 1.Todd classes
                                                                                                                                                                                                • 2.The Equivariant Riemann-Roch Theorem
                                                                                                                                                                                                  • 3.The KawasakiRiemann-RochformulaI：finiteabelianquotients
                                                                                                                                                                                                    • 4.The KawasakiRiemann-RochformulaII：torusquotients
                                                                                                                                                                                                    • Appendix J.Cobordism invariance of the index of a transversally elliptic operator by Maxim Braverman
                                                                                                                                                                                                      • 1.The SpinC-Dirac operator and the SpinC-quantization
                                                                                                                                                                                                        • 2.The summary of the results
                                                                                                                                                                                                          • 3.Transversally elliptic operators and their indexes
                                                                                                                                                                                                            • 4.Index of the operator Ba
                                                                                                                                                                                                              • 5.The model operator
                                                                                                                                                                                                                • 6.Proof of Theorem 1
                                                                                                                                                                                                                • Bibliography
                                                                                                                                                                                                                  • index

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