Smooth Manifolds and Observables
This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances. Motivating this synthesis is the mathematical formalization of the process of observation from class...
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2020, 2020
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| Edition: | 2nd ed. 2020 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Foreword
- Preface
- 1. Introduction
- 2. Cutoff and Other Special Smooth Functions on R n
- 3. Algebras and Points
- 4. Smooth Manifolds (Algebraic Definition)
- 5. Charts and Atlases
- 6. Smooth Maps
- 7. Equivalence of Coordinate and Algebraic Definitions
- 8. Points, Spectra and Ghosts
- 9. The Differential Calculus as Part of Commutative Algebra
- 10. Symbols and the Hamiltonian Formalism
- 11. Smooth Bundles
- 12. Vector Bundles and Projective Modules
- 13. Localization
- 14. Differential 1-forms and Jets
- 15. Functors of the differential calculus and their representations
- 16. Cosymbols, Tensors, and Smoothness
- 17. Spencer Complexes and Differential Forms
- 18. The (co)chain complexes that come from the Spencer Sequence
- 19. Differential forms: classical and algebraic approach
- 20. Cohomology
- 21. Differential operators over graded algebras
- Afterword
- Appendix
- References
- Index