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Viser: An Introduction to Manifolds
An Introduction to Manifolds Vital Source e-bog
Loring W. Tu
(2010)
An Introduction to Manifolds
Loring W. Tu
(2010)
Sprog: Engelsk
Detaljer om varen
- 2. Udgave
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Springer Nature (Oktober 2010)
- ISBN: 9781441974006
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Detaljer om varen
- 2. Udgave
- Paperback
- Udgiver: Springer New York (Oktober 2010)
- ISBN: 9781441973993
Chapter 1. Eudlidean Spaces.
1. Smooth Functions on a Euclidean Space.-
2. Tangent Vectors in R(N) as Derivativations.-
3. The Exterior Algebra of Multicovectors.-
4. Differential Forms on R(N).-
Chapter 2. Manifolds.-
5. Manifolds.-
6. Smooth Maps on a Manifold.-
7. Quotients.-
Chapter 3. The Tangent Space.-
8. The Tangent Space.-
9. Submanifolds.-
10. Categories and Functors.-
11. The Rank of a Smooth Map.-
12. The Tangent Bundle.-
13. Bump Functions and Partitions of Unity.-
14. Vector Fields.-
Chapter 4. Lie Groups and Lie Algebras.-
15. Lie Groups.-
16. Lie Algebras.-
Chapter 5. Differential Forms.-
17. Differential 1-Forms.-
18. Differential k-Forms.-
19. The Exterior Derivative.-
20. The Lie Derivative and Interior Multiplication.-
Chapter 6. Integration.-
21. Orientations.-
22. Manifolds with Boundary.-
23. Integration on Manifolds.-
Chapter 7. De Rham Theory.-
24. De Rham Cohomology.-
25. The Long Exact Sequence in Cohomology.-
26. The Mayer -Vietoris Sequence.-
27. Homotopy Invariance.-
28. Computation of de Rham Cohomology.-
29. Proof of Homotopy Invariance.-Appendices.- A. Point-Set Topology.- B. The Inverse Function Theorem on R(N) and Related Results.- C. Existence of a Partition of Unity in General.- D. Linear Algebra.- E. Quaternions and the Symplectic Group.- Solutions to Selected Exercises.- Hints and Solutions to Selected End-of-Section Problems.- List of Symbols.- References.- Index.