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Moment Maps, Cobordisms, and Hamiltonian Group Actions
About this Title
Victor Guillemin, Massachusetts Institute of Technology, Cambridge, MA, Viktor Ginzburg, University of California, Santa Cruz, CA and Yael Karshon, The Hebrew University of Jerusalem, Jerusalem, Israel
Publication: Mathematical Surveys and Monographs
Publication Year:
2002; Volume 98
ISBNs: 978-0-8218-0502-2 (print); 978-1-4704-1325-5 (online)
DOI: https://doi.org/10.1090/surv/098
MathSciNet review: MR1929136
MSC: Primary 53D20; Secondary 53-02, 53D50, 57R90, 57S15
Table of Contents
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Front/Back Matter
Chapters
- 1. Introduction
Part 1. Cobordism
- 2. Hamiltonian cobordism
- 3. Abstract moment maps
- 4. The linearization theorem
- 5. Reduction and applications
Part 2. Quantization
- 6. Geometric quantization
- 7. The quantum version of the linearization theorem
- 8. Quantization commutes with reduction
Part 3. Appendices
- Appendix A. Signs and normalization conventions
- Appendix 10. Proper actions of lie groups
- Appendix 11. Equivariant cohomology
- Appendix D. Stable complex and $\mathrm {Spin}^c$-structures
- Appendix E. Assignments and abstract moment maps
- Appendix F. Assignment cohomology
- Appendix G. Non-degenerate abstract moment maps
- Appendix H. Characteristic numbers, non-degenerate cobordisms, and non-virtual quantization
- Appendix I. The Kawasaki Riemann–Roch formula
- Appendix J. Cobordism invariance of the index of a transversally elliptic operator, by Maxim Braverman